The P2 Tower: Re-Neighbouring the Vertical City (MSc) by Emergent Technologies and Design [EmTech] Selected Dissertations Repository

Re-Neighboring the Vertical City

Puja Bhagat (M.Arch.), Tuoan Pan (M.Sc.), Jonathan Wong (M.Arch.)

ARCHITECTURAL ASSOCIATION SCHOOL OF ARCHITECTURE GRADUATE SCHOOL PROGRAMMES PROGRAMME: EMERGENT TECHNOLOGIES AND DESIGN YEAR: 2022-2023

COURSE TITLE: MSc. Dissertation DISSERTATION TITLE: The P2 Tower: Re-Neighboring the Vertical City STUDENT NAMES: Puja Bhagat (M.Arch.), Tuoan Pan (M.Sc.), Jonathan Wong (M.Arch.)

DECLARATION: “I certify that this piece of work is entirely my/our and that my quotation or paraphrase from the published or unpublished work of other is duly acknowledged.”

SIGNATURE OF THE STUDENT:

Tuoan Pan (M.Sc.) DATE: 22 September 2023

Puja Bhagat Puja Bhagat is an M.Arch student at the Architectural Association. Her interests lie in investigating emerging material fabrication systems and robotic processes through the intersection digital and physical environments. She is particularly interested in the union of bamboo weaving and concrete, as an act of combining a delicate, intimate craft with an industrial material.

Tuoan Pan Tuoan Pan is a M.Sc. student and has to Hong Kong many times. He is fascinated by the diversity of it. The high density of the city excites him as if he have intruded into a forest of concrete and neon lights. As the film “Chungking Express” says: “In each single day of our life, we hastily brush past strangers that mean nothing to us but utter passers-by, but as time advances, one or two from the unknown group might unconsciously become an unalienable part for us, like an intimate friend or a real confidant.”

Jonathan Wong Jonathan Wong is an M.Arch student at the Architectural Association and holds a B.Arch and B.Sc in Mathematics from Penn State University. As he sees it, mathematics should no longer be merely an analytical tool in architecture, but instead, it should further our knowledge about the field and push it into new frontiers. Therefore, he believes a new understanding about the role mathematics can play in architecture will redefine the ways in which we approach issues of sustainability.

COURSE DIRECTOR

Dr. Elif Erdine

STUDIO MASTER

Dr. Milad Showkatbakhsh STUDIO TUTORS

FOUNDING DIRECTOR

Dr. Michael Weinstock

Dr. Naina Gupta | Paris Nikitidis | Felipe Oeyen Dr. Alvaro Velasco Perez | Lorenzo Santelli | Fun Yuen

Acknowledgments The team would like to express gratitude towards everyone who supported the evolution of this thesis. The team would particularly like to thank Dr. Michael Weinstock, Dr. Elif Erdine, and Dr. Milad Showkatbakhsh, along with our tutors Dr. Naina Gupta, Paris Nikitidis, Felipe Oeyen, Dr. Alvaro Velasco Perez, Lorenzo Santelli, and Fun Yuen, for guiding us at every stage of design. Their unique insights and fruitful discussions pushed the domain of the thesis to new levels.

Table of Contents Abstract............................................................................. xi 01 Introduction.................................................................. 13 02 Domain Chapter............................................................ 15 Rise of the Tower Block........................................................................ 16 Which Public? Which Private?............................................................. 22 Quantifying the Publicness of Public Spaces................................... 23 The Private Tower Block...................................................................... 25 A Case Study of Three Hong Kong Towers.................................... 25 Visions for an Adaptive Architecture..................................................... 28 Towers and Timescales......................................................................... 30 Discussion............................................................................................ 31 Bibliography......................................................................................... 32

03 Methodology................................................................. 35 The Public-Private Evaluation Method.................................................. 36 The Parameters and Sociability Calculation Method....................... 36 Tower Organization.............................................................................. 42 The Principles of Bamboo Stems as a Structural System................ 42 Co-Evolutionary Algorithms for Private-Public Distribution.......... 43 Program Relationships......................................................................... 44 Small-world Network as a Spatial Relationship System.................. 44 Fabrication and Material System........................................................... 46 Additive Manufacturing: Robotic 3D Printing................................ 46 Material Systems:.......................................................................... 47 Fiber-Reinforced Cementitious Composites.................................... 47 Material Systems:.......................................................................... 48 Bamboo Strip Weaving as Rebar Reinforcement and Formwork...... 48 Analysis Tools...................................................................................... 50 Finite Element Analysis (FEA)...................................................... 50 Computational Fluid Dynamics (CFD)........................................... 50 Artificial Neural Network (ANN)................................................... 50 Bibliography......................................................................................... 52

04 Research Development.................................................. 55 Project Workflow.................................................................................. 56 Overview.............................................................................................. 58 4.1 Structural System Studies.............................................................. 59 4.1.1 Bamboo Internode Mathematical Expression ........................ 59 Scaling Experiment........................................................................ 59 4.2 Computational Fluid Dynamics Neural Network Experiment.... 62 4.2 Public-Private ............................................................................... 64 Distribution Studies.............................................................................. 64 4.2.1 Co-Evolutionary .................................................................. 64 Algorithm Experiments.................................................................. 64 4.3 Program Topology Studies.............................................................. 70 4.3.1 Small World Network Experiments....................................... 70

4.4 Material Fabrication ....................................................................... 74 Variable Control Studies....................................................................... 74 4.4.1 Polygon Gaussian Curvature................................................. 74 4.4.2 Strip Width / Depth Ratio.................................................... 76 4.4.3 Weave Density for 3D Printing: Material Sagging................. 78 4.4.4 Weave Density for 3D Printing: Minimal Deformation.......... 78 4.4.5 Calibration of the Robot and Woven Artifact......................... 78 4.4.6 Joint System......................................................................... 80 4.4.7 Digital to Physical Translation............................................. 81 Bibliography......................................................................................... 84

05 Design Development..................................................... 87

Overview.............................................................................................. 88 5.1 Tower Morphology.......................................................................... 90 5.2 Structural System........................................................................... 94 5.3 Private-Public Distribution............................................................. 98 5.4 Programmatic Typology................................................................. 102 5.5 Spatial Organization....................................................................... 106 Component Design......................................................................... 110 5.6 Material Fabrication System........................................................... 111 Component Material System.......................................................... 111 5.6.1 Component Weaving Pattern................................................. 112 5.6.2 Component .......................................................................... 114 Structural Analysis........................................................................ 114 5.6.3 Component Slab ................................................................... 115 Section Test................................................................................... 115 5.6.4 Large Scale Mock-Up........................................................... 117

06 Design Proposal............................................................ 119 Site Selection........................................................................................ 121 Case Study........................................................................................... 124 Application of ...................................................................................... 124 Tower Workflow................................................................................... 124 Life in the P2 Tower.............................................................................. 127 Adaptable System................................................................................. 132 Component Design......................................................................... 133 Adaptation: Months Timescale....................................................... 137 Adaptation: Months Timescale....................................................... 139 Adaptation: Months Timescale....................................................... 141 Adaptation: 1 Year......................................................................... 142 Adaptation: 3 Years....................................................................... 143 Adaptation: 5 Years....................................................................... 144 Adaptation: 10 Years..................................................................... 145

07 Discussion..................................................................... 149 Overview.............................................................................................. 150 Workflow.............................................................................................. 150 Computational Tools............................................................................. 150 Fabrication System............................................................................... 151 Case Study........................................................................................... 152 Conclusion............................................................................................ 152

List of Figures Figure 02: Shek Kip Mei Fire 1953............................................................. 16 Figure 03: Le Corbusier’s Ville Radieuse..................................................... 17 Figure 04: Map of Unauthorized Built Works across Hong Kong.................. 18 Figure 05: Evolution of the Tower Block...................................................... 18 Figure 06: Urban Density Timeline............................................................. 21 Figure 07: Spectrum of Sociability............................................................... 22 Figure 08: Kohn’s Two Dimensions of Publicness........................................ 23 Figure 09: Four Models for Evaluating Publicness....................................... 24 Figure 10: Tower Block Case Study............................................................. 25 Figure 11: Nakagin Capsule Tower by Kisho Kurokawa (1972)................... 29 Figure 12: Plug-In City by Peter Cook (1964)............................................. 29 Figure 13: Sociability Spectrum................................................................... 37 Figure 14: Sociability Evaluation System..................................................... 38 Figure 15: Sociability Parameter Calculation Method................................... 41 Figure 16: Bamboo Stem Elements.............................................................. 42 Figure 17: Mathematical Expression of Bamboo Nodes................................ 42 Figure 18: Evolutionary Algorithm Workflow.............................................. 43 Figure 19: Co-Evolutionary Algorithm Workflow........................................ 43 Figure 20: Small-World Network................................................................. 44 Figure 21: Small-World Network Equations................................................ 44 Figure 22: Small-World Network in Architecture......................................... 45 Figure 23: Fabrication System..................................................................... 46 Figure 24: Concrete Lifecycle...................................................................... 47 Figure 25: Fiber-Reinforced Cementitious Composites Lifecycle.................. 47 Figure 26: Bamboo Growth Regions............................................................ 48 Figure 27: Bamboo Growth Rate................................................................. 48 Figure 28: Bamboo Weaving........................................................................ 49 Figure 29: Artificial Neural Network (ANN)................................................ 51 Figure 30: Scope of Research Development Phase....................................... 58 Figure 31: Internode Equation Experiment Setup........................................ 59 Figure 32: Internode Equation Experiment Results...................................... 60 Figure 33: Internode Equation Experiment Post-analysis............................. 61 Figure 34: Wind Pressure ANN.................................................................. 62 Figure 35: Wind Pressure ANN Setup......................................................... 63 Figure 36: Three Types of Co-Evolution...................................................... 64 Figure 37: EA and CoEA Phenotype Comparison........................................ 65 Figure 38: Paracitism CoEA Results........................................................... 66 Figure 39: Commensalism CoEA Results..................................................... 67 Figure 40: Mutualism CoEA Results............................................................ 68 Figure 41: Small World Network Concept.................................................... 70 Figure 42: Small World Network Evolutionary Algorithm Set-up................. 71 Figure 43: Small World Network Evolutionary Algorithm Results............... 72 Figure 44: Polygon Gaussian Curvature: Experiment Results....................... 74 Figure 45: Polygon Gaussian Curvature: Woven Samples............................. 75 Figure 46: Strip Width to Depth Ratio: Experiment Results......................... 76 Figure 47: Strip Width to Depth Ratio: Woven Samples............................... 77 Figure 48: Weaving Density: Material Sagging Experiment Results (4.4.3). 79 Figure 50: Weaving Density: Deformation Experiment Results (4.4.4)........ 79

Figure 49: Weaving Density for 3D Printing: Woven Samples..................... 79 Figure 51: Parallel and Perpendicular Joint Systems.................................... 80 Figure 52: Digital to Physical Translation................................................... 81 Figure 53: Physically Woven Samples.......................................................... 82 Figure 54: Difference in Gaussian Curvature............................................... 82 Figure 55: Digitally Woven Samples............................................................ 83 Figure 56: Difference in Strip-to-Depth Ratio.............................................. 83 Figure 57: Scope of Design Development Phase........................................... 88 Figure 58: Tower Design Workflow............................................................. 89 Figure 59: Tower Morphology Evolutionary Algorithm Set-up..................... 91 Figure 60: Tower Morphology Evolutionary Algorithm Results.................... 92 Figure 61: Structural System Evolutionary Algorithm Set-up...................... 95 Figure 62: Structural System Evolutionary Algorithm Results..................... 96 Figure 63: Public-Private Distribution Evolutionary Algorithm Set-up........ 99 Figure 64: Public-Private Distribution Evolutionary Algorithm Results....... 100 Figure 65: Programmatic Topology Evolutionary Algorithm Set-up............. 103 Figure 66: Programmatic Topology Evolutionary Algorithm Results............ 104 Figure 67: Spatial Organization Evolutionary Algorithm Set-up.................. 107 Figure 68: Spatial Organization Evolutionary Algorithm Results................. 108 Figure 69: Component Morphology and Placement...................................... 110 Figure 70: Material Fabrication System....................................................... 111 Figure 71: Weaving Pattern Influence from Experiments............................. 112 Figure 72: Component Weaving Experiment Results.................................... 112 Figure 73: Component Structural Analysis.................................................. 114 Figure 74: Component Slab Test Model........................................................ 115 Figure 75: Workflow Applied to Case Study................................................ 125 Figure 76: Life in the P2 Tower.................................................................... 127 Figure 77: Adaptability of the P2 Tower....................................................... 132 Figure 78: Component Design..................................................................... 133 Figure 79: Exploded View of Component System......................................... 135 Figure 80: View of Working Space.............................................................. 137 Figure 81: View of Restaurant..................................................................... 139 Figure 82: View of Library.......................................................................... 141

Abstract Over time, people’s sociability changes, yet the buildings they occupy do not change to accommodate their new needs. Densification has increased this problem, particularly in Hong Kong. In Hong Kong, rapid densification focused solely on private spaces, leading to the proliferation of the Hong Kong tower block typology. Yet, the rigidity of the tower block typology prevents spaces from meeting people’s sociability needs as they change over time. Thus, the P2 Tower operates in this gap between the social affordance of the Hong Kong tower block and the people’s sociability needs. It offers a new housing solution that meets the density needs of cities while also facilitates continuous spatial changes to match the private and public demands of people over time. The P2 Tower engages the concepts of private and public narrowly through a lens of sociability to develop a system for quantifying the sociability of a space. Such a system underpinned the development of a novel computational framework which employs biomimetic principles alongside algorithmic process. The framework deconstructs the tower into its component systems, developing them as individual parts of a whole. The tower morphology and structural system act as fixed elements and are optimized for the climate conditions and high wind loads of Hong Kong by employing evolutionary algorithms, artificial neural networks, and abstracted principles of a bamboo stem. On the other hand, the distribution of private and public spaces, the programmatic topologies, and the spatial organization are flexible elements which continuously adapt across the timescales of decades, years, and months respectively. Such adaptation is enabled by an advanced fabrication system that combines bamboo weaving techniques and concrete 3D printing. Together, this dynamic framework enables the P2 Tower to continuously adapt at varying scales of time and space in response to people’s shifting sentiments around sociability.

The P2 Tower

13 Bhagat | Pan | Wong

This thesis addresses the dual but interrelated domains of densification and sociability by proposing a model for evaluating a space along the publicprivate spectrum and then using this methodology as a driving force to develop a new tower system workflow focused on its occupants’ sociability. Thus, a level of adaptation is integrated into the system following the logic of this framework, allowing towers to exhibit different functionalities and performances over time.

01 Introduction

While this thesis applies its framework to Hong Kong as a case study, there is potential to implement its roots to other dense cities around the globe. As such, the research challenges the traditional notion of the tower block as a permanent, unchanging structure in the built environment and discover its potential to become a temporal system which evolves alongside its occupants, meeting their needs and improving urban livability. Only in this way, can architecture begin to address the complex challenges of densification.

02 Domain Chapter

2.1 Rise of the Tower Block 2.2 Which Public? Which Private? 2.3 The Private Tower Block 2.4 Visions for an Adaptable Architecture 2.5 Towers and Timescales

The P2 Tower

Rise of the Tower Block The Shek Kip Mei fire of 1953 marked a significant paradigm shift in the way the Hong Kong government approached the redevelopment of land and public housing. As tens of thousands of residents were abruptly homeless, the government raced to meet their immediate needs and provide basic shelter. Yet, the government also viewed this moment as an opportunity to revolutionize the land usage of its ‘barren rock’ and sharply alter government policy.1 Where sprawling squatter huts once hugged the earth, multi-story tower blocks were constructed that soared towards the sky. Thus, the seeds of the world’s largest housing program were planted, and the tower block typology became synonymous with identity of Hong Kong. The newly constructed tower blocks housed 2,500 residents; five people lived in an apartment; and each apartment averaged 24 m2.2 Michael Suen Ming-yeung, Secretary for Housing, Planning and Lands, described these tower blocks as “simple, low-cost shelters to a minimum standard to meet the emergency needs.”3 As fires in dense squatter settlements plagued Hong Kong throughout the 1950’s and 1960’s, the emergency response demanded the construction of more and more tower blocks across the city, culminating in the formulation of the Ten-Year Housing Program in 1973. The program aimed to provide 1.8 million Hong Kong residents with “adequate housing” which was permanent and self-contained.4 It was an ambitious program, but dense public housing was nothing innovative in 1973. Through this public housing program, the Hong Kong government tapped into a global trend

for mass housing which emerged in response to mass migration to urban areas and rose to prominence following the destruction of World War II. Modern mass migrations began in the late 1800’s and early 1900’s, causing cities to rapidly densify.5 Over time, rapid densification only became worse, creating a strain on urban environments, forcing architects and urban planners to develop a new housing typology: the mass housing tower block.6 The tower block was designed based upon two principles which emerged at the time: industrial standardization and housing as a basic human right.7 Through these principles, the tower block enabled urban cities to efficiently house as many individuals

Figure 02: Shek Kip Mei Fire 1953

as possible in a small urban footprint. Many architects around the world, such as Le Corbusier in France, Leonid Sabsovich in Russia, and Bruno Taut in Germany, adopted these principles and developed their own tower block morphologies in response to the particular urban density issues in their cities.8 Thus, the tower block took its place as the archetypal typology for rapidly densifying cities across the globe.

Fung Ping Yan, “Public Housing in Hong Kong Past, Present and Future” (Chartered Institute of Housing Asian Pacific Branch, 2006), 2. 2 Ping Yan, “Public Housing in Hong Kong Past, Present and Future”, 3. 3 Alan Smart, The Shek Kip Mei Myth: Squatters, Fires and Colonial Rule in Hong Kong, 1950 - 1963 (Hong Kong: Hong Kong University Press, 2006), 1. 4 Ying Deng, Edwin H.W. Chan, and S.W. Poon. “Challenge-Driven Design for Public Housing: The Case of Hong Kong.” Frontiers of Architectural Research 5, no. 2 (2016): 213–224. https://doi.org/10.1016/j.foar.2016.05.001. 5 Charles More, Understanding the Industrial Revolution, (London: Routledge, 2000), 1. 6 Florian Urban, Tower and Slab: Histories of Global Mass Housing (London: Routledge, 2012): 10-11. 7 Urban, Tower and Slab, 2. 8 Urban, Tower and Slab, 7-8. 1

17 Bhagat | Pan | Wong

Figure 03: Le Corbusier’s Ville Radieuse

Surprisingly to some and less so to others, the housing block typology fell out of prominence in the United States and Europe as rapidly as it had risen to it due to its failures anthropologically. Unfulfilled promises for community and modernity gave way for realities of social isolation, class segregation, and inhumane infrastructure.9 In essence, the tower block typology failed to meet the immediate and future needs of its residents. These discontinuities were not the result of poor problem solving or lackluster ambitions, but instead due to an overemphasis of the architectural design on the private, as opposed to the public. Such a focus on the private was the result of the tower block being a mechanism for solving a problem as opposed to planning for the future. Mass migration required housing, so housing is what the government built, nothing more or less. Thus, these structures were unable to adapt to the changing needs of the residents and society over time. Yet, even as other cities sought new solutions to urban densification, the Hong Kong government embraced the tower block typology, resulting in its proliferation across Hong Kong. In 1997, the Hong Kong government pledged to construct “on average not less than 85,000 flats per year.”10 By 2013, the tower block encapsulated 46.7% of the total housing stock in the city, a figure which only continues to grow today due to persistent urban strain.11 Such a legacy created a fixation on the private individual, and Hong Kong’s regulatory frameworks for housing embodied such a notion. In the LongTerm Housing Strategy (LTHS), the Hong

Kong government defined “adequate housing” by five characteristics: 1. Built of permanent materials 2. Self-contained 3. Occupied on an unshared basis except in the case of very small households 4. Not overcrowded 5. At a rent or price within the household’s means.12 Such a definition failed to make any reference to public spaces and inherently focused on providing for the private individual by directly contradicting the idea that a person exists amongst others. These principles remained pillars of public housing throughout time, resulting in minimal changes to the ways in which the tower block addressed the relationship between private and public. As the tower block matured from the initial Mark I type to the modern Harmony model over 50 years, the Hong Kong government gradually acknowledged the significance of community services to housing, but these were simply relegated to the ground floor or detached within the surrounding site.13 Thus, the tower blocks remained as housing for housing instead of becoming housing for living, and the sociability needs of the residents remained unfulfilled in their daily lives. These unfulfilled needs forced residents to create their own spaces for sociability. Across Hong Kong, residents living in tower blocks attached appendages onto the facade to hold air conditioning units, built caged-in balconies to extend their living units, and constructed entire

Constance Smith and Saffron Woodcraft. “Tower Block ‘Failures’?: High-Rise Anthropology.” Focaal 2020, no. 86 (2020): 1–10. https://doi.org/10.3167/fcl.2020.860101. 10 Ping Yan, “Public Housing in Hong Kong Past, Present and Future”, 5. 11 Deng et al., “Challenge-Driven Design for Public Housing: The Case of Hong Kong,” 213–224. 12 Lau, Kwok-yu. Housing In the Other Hong Kong Report. (Hong Kong, 1991), 347-348. 13 Deng et al., “Challenge-Driven Design for Public Housing: The Case of Hong Kong,” 213–224. 9

The P2 Tower

Figure 05: Evolution of the Tower Block

rooftop structures to gamble and congregate.14 The proliferation of these homemade structures, labeled unauthorized built works (UBW) by the Hong Kong Housing Authority, reflect an unmet demand by residents for spaces of sociability.15 In 2001, an estimated 800,000 unauthorized built works existed across Hong Kong which stood in contrast to the 810,468 public rental housing units built today.16,17 By mapping the locations of these unauthorized built works alongside the density of Hong Kong and the locations of the public housing estates,

the entwined relationship between the tower block typology and these structures becomes evident. Not only their existence, but also the widespread proliferation of these UBWs across Hong Kong point towards a major discrepancy between the permanence of the existing tower block typology and the shifting temporality of people’s lives. At its core, the tower block typology in Hong Kong failed to meet people’s sociability needs as they change over time by prioritizing the private individual over of the public collective.

Tower Blocks Unauthorized Building Works (UWB) >40,000p/km2 2

40,000p/km2

25,000p/km2

4 5

2 2

4 2

2 39 3

5 6

18 17 2

67 6

52 5

20 37

2 4

6 31 97

19 4

13 47 55

8 7

2 4 14

16 12

2 3

<4,000p/km2

10,000p/km2

10 15

55 3

12 4

9 9

2 3 8

Figure 04: Map of Unauthorized Built Works across Hong Kong

Francisco García Moro. “The Death and Life of Hong Kong’s Illegal Façades.” ARENA Journal of Architectural Research 5, no. 1 (2020): 2. https://doi.org/10.5334/ajar.231. 15 Daniel Chi Wing Ho, Kwong Wing Chau, and Yung Yau. “Evaluating Unauthorized Appendages in Private Apartment Buildings.” Building Research & Information 36, no. 6 (2008): 568–579. https://doi.org/10.1080/09613210802386198. 16 Lawrence W.C. Lai and Daniel C.W. Ho. “Unauthorised Structures in a High‐rise High‐density Environment ‐ The Case of Hong Kong.” Property Management 19, no. 2 (2001): 112–23. https://doi.org/10.1108/02637470110387830. 17 Hong Kong Housing Authority, “Key Figures,” Hong Kong Housing Authority, Hong Kong Housing Authority, 31 March 2022 14

FRENCH REVOLUTION

rise of tec

Georges Haussmann Paris, France

downfall of cities

1920-1930

PARIS BOULEVARDS

1882

1853-1870

rise of political uprisings

Ebenezer Howard Great Britain

Glob

1929 - 1939

rise of poor health in cities

THE GARDEN CITY

WORLD

Global

1914 - 1918

rise of pollution

1850-1920

rise of technology

Global

1789 / 1830 1848 / 1871

Paris, France

1820 - 1840

Great Britain

GREAT DEPRESSION

WORLD WAR I

RADIANT CITY

1931

INDUSTRIAL REVOLUTION

BROADACRE CITY Frank Llyod Wright United States

Le Corbusier Paris, France

THE LINEAR CITY Arturo Soria y Mata Madrid, Spain

THE DEATH AND AMERICA

Jan Unit

United States

chnology

2001

1959 - 1975

China

1960-70

1970

rise of social distancing

SERPENTONE Mario Florentino Rome, Italy

PLUG-IN CITY

1961

2015-2023

Archigram United Kingdom

1960-70

ne Jacobs ted States

Global

rise of security and surveillance rise of communal living

D LIFE OF AN CITIES

COVID-19 PANDEMIC

2021 - 2022

9/11 TERRORIST ATTACK

CULTURAL REVOLUTION

Global

1950 - 1953

Global

1938 - 1945

bal

VIETNAM WAR

1966 - 1976

WAR II KOREAN WAR

CAPSULE TOWER

15 MINUTE CITY

The Metabolists Ginza, Japan

Carlos Moreno Paris, France

Figure 06: Urban Density Timeline

The P2 Tower

Which Public? Which Private?

0.0

1.0

PRIVATE

PUBLIC

INDIVIDUAL

COLLECTIVE

STATIC

ACTIVE

ISOLATED

CONNECTED

Figure 07: Spectrum of Sociability

While the history of the tower block in Hong Kong presents strong evidence for characterizing the tower blocks of Hong Kong as an architecture of and for the private, the research would be remiss if it were to make such a bold assertion without acknowledging the pervasiveness of complexity and contradiction in the terms public and private. Therefore, it is imperative to first break down these terms and explore their evolution and divergence over time before being able to properly address how they might manifest architecturally. And so, the research narrowly examines these two terms through the lens of architecture while maintaining an awareness of the parallel conversations occurring in other disciplines such as sociology, philosophy, and political science. The concept of a public space or a private space is one often taken for granted and misused. Misused by architects, planners, and developers, the colloquial, idealization of these concepts is typically not reflective of reality. The Italian philosopher Noberto Bobbio declared in 1989

that the distinction between these two terms was one of the “grand dichotomies” of Western philosophy.18 However, such a unitary division overlooked the lenses through which the terms were utilized. It assumed a strict political division.19 In reality, the relationship between these terms is neither political nor apolitical. It is instead dependent on the realm of discourse in which they are employed. Sociologist Jeff Weintraub identified in 1997 four overarching categories through which the terms adopt unique definitions, providing a framework for this research to define its scope. In particular, Weintraub’s dramaturgic approach reflects emerging, modern concepts of public and private in the realm of architecture. He explains that “the [dramaturgic] approach… sees the “public” realm as a sphere of fluid and polymorphous sociability and seeks to analyze the cultural and dramatic conventions that make it possible.”20 Such a definition defines space along a spectrum of sociability which is influenced by the ways in which people interact

Norberto Bobbio, Democracy and Dictatorship: The Nature and Limits of State Power (Minneapolis, MN, 1989), 1. Jeff Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy (New York, NY, 1997), 2. 20 Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy, 7. 18

23 Bhagat | Pan | Wong

Figure 08: Kohn’s Two Dimensions of Publicness

it. Sociability, as Jane Jacobs illustrates, is the result of the configuration of physical spaces. In The Death and Life of Great American Cities (1961), Jacobs describes how the “streets of great cities have built-in equipment allowing strangers to dwell in peace together on civilized but essentially dignified and reserved terms. Lowly, unpurposeful and random as they may appear, sidewalk contacts are the small change from which a city’s wealth of public life may grow.”21 Yet, such a strictly architectural perspective oversimplifies the discussion by ignoring the broader factors at play in a neighborhood, city, or society. Therein lies the intricacies of Weintraub’s dramaturgic approach. He acknowledges the multi-dimensionality of the public-private distinction, arguing that only through “the interplay between the spatial organization of cities and long-term sociohistorical processes” may a fuller understanding of public and private emerge.22 While architects cannot control all these external elements, it is imperative for them to have an awareness of these social relationships.

Quantifying the Publicness of Public Spaces Building out from Weintraub’s dramaturgic approach, the political scientist Margaret Kohn evoked a new idea by challenging the established, mono-dimensional definitions of public and private by architects and set a

qualitative baseline for distinguishing types of spaces along a spectrum between public and private.23 Kohn illustrated how one may begin to approach quantifying the publicness of a public space, hybridizing the physical, social, and political aspects of a space. While her approach to public space was novel, it lacked the specificity and rigor necessary to compare and evaluate the effectiveness of a space to be public or private. It was vague, ambiguous, and remained open to interpretation. Such characteristics continued to plague definitions by other researchers. Four models for publicness emerged over the following decade which achieved increasingly levels of specificity and rigor. In 2007, Van Melik, Van Aalst, and Van Weesep developed the cobweb model, which addressed public space indirectly by focusing on ‘themed space’ and ‘secured space’.24 The model utilized a series of six radial spokes and three concentric rings to visually represent the intensity for each dimension of themed and secured spaces: surveillance, restraints on loitering, regulation, events, funshopping, and pavement cafes.25 The strength of the cobweb model lied in its multi-dimensional visual representation of publicness. Building upon the cobweb model, Nemeth and Schmidt created the tri-axial model in 2010, which directly focused on establishing a distinction between public and private.26 The model utilized three intersecting axis, where each axis represented a different dimension of publicness: ownership, management, and use/ users.27 Though this model, the publicness of

Jane Jacobs, The Death and Life of Great American Cities (New York, NY, 1961), 72. Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy, 24. 23 Kohn, Brave New Neighborhoods: The Privatization of Public Space, 11 24 Rianne Van Melik, Irina Van Aalst, and Jan Van Weesep. “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space.” Journal of Urban Design 12, no. 1 (2007): 25–42. https://doi.org/10.1080/13574800601071170. 21 22

Németh and Schmidt (2010) each dimension is identified along a continuum, providing a more intuitive comparison.

Van Melik, Van Aalst, Van Weesep (2007)

24 The P2 Tower

Ownership

Uses/Users

More ‘public’

More ‘private’

5 Van Melik, Van Aalst, Van Weesep (2007) Secured public space Themed public space 1. Surveillance 1. Events 2 2. 2. Restrains on lotering Funshopping 3. Regulation 3. Pavement cafes

2007)

Ownership

Uses/Users

Németh and Schmidt (2010) Ownership

6 3

More ‘private’

Management

5 Varna and Tiesdell (2011)

Secured public space Themed public space 1. Surveillance 1. Events A on lotering 2. Space Restrains 2. Funshopping More ‘public’ 3. Regulation 3. Pavement cafes

Ownership

More ‘private’

Space B

pace

Physical Németh and Schmidt (2010) Conﬁguration

ing cafes

Ownership

2007)

Control

More Public

Uses/Users

Management

Varna and Tiesdell (2011) Space A Animation

More ‘public’ Ownership

Civility

More ‘private’

Space B Physical Langstraat and Van Melik (2013) Conﬁguration

space

Control

Management

Ownership

Control More Public

More Private

Animation

Civility

Langstraat and Van Melik (2013) Civility

Acessibility

Inclusiveness

Ownership

Management

Control More Public

Acessibility

Civility

More Private

Acessibility

Inclusiveness

Ownership

Management

As a whole, these four models offered a solid basis for understanding how the publicness of a space may be evaluated. Yet, they all lacked three critical elements. Firstly, they primarily relied on qualitative measurements and data, making comparisons between different spaces either unreliable or inconsistent. Secondly, Inclusiveness Acessibility each model was constructed as a methodology for post-analyzing an existing space as opposed to designing new spaces. Lastly, all of the models approached the distinction between public and private from a biased lens of publicness, relegating the concept of private to mean anything else but public. These missing elements constitute the foundation from which this research began to construct its own model for evaluating a space along a spectrum from private to public, from the individual to the collective, from the personal to the social. More Public

ing

cafes Ownership

Ownership

Management

More ‘public’

Uses/Users

Management

In 2011, Varna and Tiesdell reconciled the cobweb and tri-axial models. The star model, Space A as they called it, was arranged along five spokes extending out from a hexagon, each Space B spoke representing a dimension of publicness: ownership, civility, physical Németh and Schmidt (2010) control, configuration, animation.28 It was the first time that a model for publicness considered the physical characteristics of a space. Additionally, the model utilized a systematic process for Space A quantifying the publicness of a space through identifying, weighting, and combining to Space B create a single meta-dimensional score. In 2013, Langstraat and Van Melik developed Langstraat and Van Melik (2013) the OMIA model to articulate the publicness of Management aOwnership public space as a result of privatization.29 It utilized concentric circles subdivided into four quadrants, each representing one dimension of publicness: ownership, management, accessibility, and inclusiveness. This model realigned with Weintraub’s original concept of sociability and broadened the applicability of a Langstraat and Van Melik (2013) publicness evaluation model.

More Private

Inclusiveness

Figure 09: Four Models for Evaluating Publicness

Van Melik et al., “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space,” 25. Jeremy Németh and Stephen Schmidt. “The Privatization of Public Space: Modeling and Measuring Publicness.” Environment and Planning B: Planning and Design 38, no. 1 (2011): 5–23. https://doi.org/10.1068/b36057. 27 Németh and Schmidt, “The Privatization of Public Space: Modeling and Measuring Publicness,” 5. 28 George Varna and Steve Tiesdell. “Assessing the Publicness of Public Space:The Star Model of Publicness.” Journal of Urban Design 15, no. 4 (November 2010): 575–598. https://doi.org/10.1080/13574809.2010.502350. 29 Florian Langstraat and Rianne Van Melik. “Challenging the ‘End of Public Space’: A Comparative Analysis of Publicness in British and Dutch Urban Spaces.” Journal of Urban Design 18, no. 3 (2013): 429–48. https://doi.org/10.1080/13574809.2013.800451. 25 26

The Private Tower Block

The Sociability Spectrum, as the research has coined it, is an adaptive model for evaluating the publicness of a space through a set of quantifiable parameters which fall under the scope of an architect’s work as a designer. It builds upon the four previous models for publicness by specifically focusing on their three identified weakness. Without delving into too much detail about the model itself, which will be further articulated and explained in Chapter 02, the Sociability Spectrum evaluates a space by analyzing four dimensions of publicness: Ownership, Accessibility, Affordance, and Environment. Each dimension has its own unique set of quantifiable parameters which score on a normalized range. The research conducted a case study of three archetypal Hong Kong tower blocks to evaluate their score along the Sociability Spectrum and tune the system to the context of Hong Kong. The Mark I (1955), Linear I (1980), and Harmony I (2000) tower block types were selected to explore the evolution of the tower block’s sociability throughout time. The study determined that the towers had sociability scores of 0.18, 0.17, and 0.20 respectively.

LINEAR I

DENSE APARTMENT LAYOUT B.02 Occupant Density B.05 Average Area / Space

40m

LACK OF PROGRAM VARIETY

B.03 Spatial Connectivity

B.06 Function Density

Figure 10: Tower Block Case Study

PRIVATE

SA = 0.40

EN = 0.18

OW = 0.08

PUBLIC

BA = 0.12

40m

0.20

PRIVATE

SA = 0.36

OW = 0.08

PUBLIC

EN = 0.15

0.17

PRIVATE

SA = 0.41

LENGTHY CORRIDORS

0.18

BA = 0.12

2000

B.01 Threshold Condition

PUBLIC

EN = 0.21

HARMONY I

LIMITED ENTRY POINTS

1980

OW = 0.08

1955

Upon further analysis, such a consistently private scores can be attributed to several major design pitfalls. Firstly, all three structures exhibited high occupant densities, resulting in only five or six square meters for each resident. Secondly, the high density also led to lengthy corridors, which drastically decreased each building’s spatial connectivity and interior daylighting. Lastly, each building lacked any program variety, meaning that occupants were required to venture out into the city to obtain daily necessities. As such, the case study revealed that while the Hong Kong Housing Authority did make form-based alterations to the tower block over time, these modifications had no evident effect on the publicness of the spaces, creating a discontinuity between the tower block and the sociability needs of the residents over time.

BA = 0.15

MARK I

Such low scores emphasized the privateness of these designs. Beyond that, it highlighted the fact that there was no significant change in the towers’ publicness, where scores differed by a mere 0.03, even though the design of the tower block changed.

Bhagat | Pan | Wong

A Case Study of Three Hong Kong Towers

The P2 Tower

Visions for an Adaptive Architecture While the tower block typology became a major vehicle for addressing modern challenges of densification in Hong Kong and around the globe, it was by no means the only means the only solution conceived and put forth by architects and urban planners during the 20th century. In fact, the practicality of the tower block stood in juxtaposition to the idealism of design proposals from the same period which envisioned an architecture which reflected the changing sociality of everyday life. Whereas one sought to solve an immediate problem, the others aimed to reimagine the ways in which we live and interact with one another. The work of Archigram and Metabolism in the 1960’s proposed a radically new solution to the challenges of mass migration and densification in the United Kingdom and Japan, respectively. These groups viewed architecture not as static and permanent objects existing within an urban context but instead as everchanging spaces integral to the urban vitality of a city.30 Through their proposals, Archigram and Metabolism experimented with architectural artifacts which were designed to change and adapt to the shifting lifestyles of its inhabitants. The Metabolists responded to the same urban conditions and densification challenges in Japan that existed in Hong Kong during the proliferation of tower block typology, yet this group looked towards the future of urban living instead of the present. The population of Tokyo tripled following World War II, raising from 2.78 million in 1945 to 8.31 million in 1960.31 The Metabolists viewed such challenges not as ones to be solved per say but instead as an opportunity to reimagine the relationship between humans and the built environment. In their manifesto, Metabolism – a Proposal for a New Urbanism (1960), the Metabolists declared that humans exist together as a continuously shifting, social entity.32 Additionally, it regarded the built

environment as an extension of this humanity.33 By intertwining these two groups and perceiving them as always in flux, the Metabolists proposed architectural artifacts which were structured to change throughout time. While a majority of the work by the Metabolist was relegated to speculative models and drawings, the Nakagin Capsule Tower by Kisho Kurokawa was realized as a built project. Conceptually, the building was designed as series of modular units attached to a central core. These modular units, or capsules, enabled continuous replicability and adaptability amongst different parts of the building as renovations were required, technology was updated, and spaces become obsolete.34 Unfortunately, such an idealism was never fully realized due to limitations of existing technology. In the United Kingdom, a similar housing crisis took place in the 1960’s, which prompted the government there to take a similar, impulsive response as the Hong Kong government. The government constructed dozens of public housing tower blocks across the country. The problem was solved but at the expense of urban livability. Rejecting the rigidity and inhumanity of the tower block, Archigram proposed an architectural system which reimagined the ways in which humans interacted with one another. Adaptation sat at the heart of Archigram’s proposal Plug-In City (1964), which took inspiration from their avant-garde counterparts in Japan. Conceptually, the project proposed private, modular residential units which plugged into a public, central infrastructure, challenging the relationship between public and private spaces in an urban context.35 Through such a system, the Plug-In City had the ability to continuously evolve programmatically, functionally, and socially. Such an evolution, as Peter Cook intended, was driven by the users’ interactions with the architecture around them.

Gizem Deniz Guneri, “Peter Cook Beyond Archigram: Towards a Critical Utopianism.” Prostor 28, no. 1 (59) (June 30, 2020): 130–41. https://doi.org/10.31522/p.28.1(59).8. 31 Hein et al., Rebuilding Urban Japan After 1945, 55. 32 Kiyonori et al., Metabolism – A Proposal for a New Urbanism (Tokyo: Bijutsu Shūpansha, 1960), 1. 33 Kishō Kurokawa, Metabolism in Architecture (London: Studio Vista, 1977), 27. 34 Kishō Kurokawa, Metabolism in Architecture, 32. 30

29 Bhagat | Pan | Wong

Figure 11: Nakagin Capsule Tower by Kisho Kurokawa (1972)

Figure 12: Plug-In City by Peter Cook (1964)

Archigram understood “housing as a consumer project,” which propelled them to design in such a way that all residents participated in constructing the sociability of their spaces through their own efforts.36 Thus, when faced

Simon Sadler, Archigram: Architecture without Architecture, 37. Simon Sadler, Archigram: Architecture without Architecture, 37.

35 36

with similar housing crises and densification challenges as Hong Kong in their respective cities, both the Metabolists and Archigram presented a vision of architecture that was organic, dynamic, and everchanging.

The P2 Tower

Towers and Timescales The visions put forth by Archigram and the Metabolists for the past, present, and future of urban living surely pushed the boundaries on how architects and urban planners may begin to understand high-rise housing in the modern era. The stark contrast of their designs with the rigidity and inhumanity of the tower block typology presents an opportunity for this thesis to propose a new housing tower that meets the immediate density needs of a city while also enabling the continuous adaptation to the changing needs of its residents over time. Before such an endeavor can be undertaken, it would be important to first investigate the layers and organization strategies of tall buildings, recognizing their unique architectural, mechanical, and structural requirements. Such a foundational understanding of towers would enable this thesis to reasonably reconcile the idealism of Archigram and the Metabolists’ megastructures and the practicality of the tower block. While tall buildings afford ample opportunity to address modern challenges of densification and urban living, the complexity of their programmatic organization and environmental conditions give rise to new challenges. Technologically, the design of a tower can be organized into five subsystems: the structural systems, the floor systems, the vertical circulation system, the façade system, and the environmental system.37 The structural system refers to the elements of the tower which are primarily responsible for resisting the vertical and lateral loads acting upon the building. Critical design aspects of a tower’s structural system to resist to wind, gravity, seismic loads include the dynamic properties, aerodynamic characteristics, location of structural members on the floor plate, the floor-to-floor heights, and the slenderness.38 The floor system refers to the elements of the building which handle horizontally transferring live and dead loads to the primary structural system for vertical transfer to the ground. The vertical circulation system refers to elements of the building which move people and goods

throughout the height of the tower. It plays a critical role particularly in mixed-use towers as a means to efficiently control the movement of people throughout the tower for their intended purposes.39 The façade system refers to the delineation between the inside and the outside and plays a major role in defining the visual aesthetics of the tower per the design intent. Additionally, the façade system is integrally connected to the structural system as it deals with high wind loads, which typically results in the façade being divided into different zones to respond to varying wind loads.40 Lastly, the environmental system refers to the ways in which the building form and the building envelope regulate the interior environmental conditions by managing the wind, rain, sunlight, etc. This includes design considerations such as the morphology, orientation, and façade elements.41 These five layers work together as independent parts of the same whole, but from a broader perspective, each layer also operates on its own timescale. Whereas the structural system of a building may be expected to operate on the timescale of centuries, the façade system only acts on the timescale of decades. Such variation brings about different influences on the design of a space such as functional requirements, spatial needs, or social perceptions. Therefore, it is critical to breakdown the timescales of each tower layer as a means to respond appropriately to its specific public and private influences. In doing so, this thesis begins to understand the ways in which architectural responses to change over time affect the sociability of a space at varying timescales. From a social perspective, the timescales of these tower layers correspond directly to the timescales of the residents, whether that is an individual, a group, or a population. For example, an individual timescale corresponds to the different stages of life. When a person is growing up, their spatial needs and connections vary drastically. Therefore, the interplay between the timescales of the layers of a tower and the lives of its residents

Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems.” (PhD, Architectural Association School of Architecture, 2014), 39. 38 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 45. 39 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 59. 40 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 62. 41 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 69. 37

Discussion

This thesis adds to the existing discourse surrounding sociability and adaptability in architecture by leveraging the power of both unique but interconnected fields to address the emerging challenges of densification and

people’s changing sociability needs in Hong Kong. The research addressed the following questions: 1. How can a novel computational framework and material fabrication system address the constant flux of people’s sociability along the public-private spectrum in Hong Kong over time? 2. How can adaptable architecture improve the quality of life in Hong Kong? 3. Can challenging conventional tower organizations in terms of public and private redefine the ways in which people live? As such, the research aimed to challenge the traditional notion of the tower block as a permanent, unchanging structure in the built environment and discover its potential to become a temporal system which evolves alongside its occupants, meeting their needs and improving urban livability. Only in this way, can architecture begin to address the complex challenges of densification.

Bhagat | Pan | Wong

The current context of the Hong Kong tower block reveals a large discrepancy between the permanence of the built environment and the temporality of people’s lives. At its core, the tower block typology in Hong Kong has failed to meet people’s sociability needs as they change over time by emphasizing the private individual over of the public collective. Therefore, this thesis investigated this gap between the social affordance of the Hong Kong tower block and the people’s sociability needs. It aimed to create a new design for public housing towers that meets the density needs of Hong Kong while also facilitating continuous spatial changes to match the needs of people over time. This is achieved by first constructing a new model for evaluating a space along the public-private spectrum. This model is then utilized as a driving force to design a new tower system workflow focused specifically on the sociability needs of its occupants. Finally, a level of adaptation is integrated into the system following the logic of this methodology, allowing towers to exhibit different functionalities and performances over time.

The P2 Tower

Bibliography Caldeira, Teresa, and Michael Sorkin. “Variations on a Theme Park: The New American City and the End of Public Space.” Journal of Architectural Education (1984-) 48, no. 1 (September 1994): 65. https://doi.org/10.2307/1425310. Deng, Ying, Edwin H.W. Chan, and S.W. Poon. “Challenge-Driven Design for Public Housing: The Case of Hong Kong.” Frontiers of Architectural Research 5, no. 2 (June 2016): 213–224. https://doi.org/10.1016/j.foar.2016.05.001. Di Palma, Vittoria, Diana Periton, and Marina Lathouri, eds. Intimate Metropolis. London: Routledge, 2008. Erdine, Elif. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems” PhD, Architectural Association School of Architecture, 2014. García Moro, Francisco. “The Death and Life of Hong Kong’s Illegal Façades.” ARENA Journal of Architectural Research 5, no. 1 (July 20, 2020): 2. https://doi.org/10.5334/ajar.231. Guneri, Gizem Deniz. “Peter Cook Beyond Archigram: Towards a Critical Utopianism.” Prostor 28, no. 1 (59) (June 30, 2020): 130–41. https://doi.org/10.31522/p.28.1(59).8. Harris, Jose. “War and Social History: Britain and the Home Front during the Second World War.” Contemporary European History 1, no. 1 (March 1992): 17–35. https://doi.org/10.1017/ S096077730000504X. Hein, Carola, Jeffery Diefendorf, and Ishida Yorifusa. Rebuilding Urban Japan After 1945. 1st ed. 2003. New York, NY: Palgrave Macmillan, 2014. Ho, Daniel Chi Wing, Kwong Wing Chau, and Yung Yau. “Evaluating Unauthorized Appendages in Private Apartment Buildings.” Building Research & Information 36, no. 6 (December 2008): 568–79. https://doi.org/10.1080/09613210802386198. Hong Kong Housing Authority, “Key Figures,” Hong Kong Housing Authority, Hong Kong Housing Authority, 31 March 2022, https://www.housingauthority.gov.hk/mini-site/ haar2122/en/index.html Kelly, G., Robert Schmidt, A. Dainty, and Victoria Story. “Improving the Design of Adaptable Buildings Though Effective Feedback in Use,” 2011. https://hdl.handle.net/2134/26294. Kiyonori et al. Metabolism – A Proposal for a New Urbanism. Tokyo: Bijutsu Shūpansha, 1960. Kurokawa, Kishō. Metabolism in Architecture. London: Studio Vista, 1977. Kohn, Margaret. Brave New Neighborhoods: The Privatization of Public Space. New York, NY: Routledge, 2004. Lai, Lawrence W.C., and Daniel C.W. Ho. “Unauthorised Structures in a High‐rise High‐density Environment ‐ The Case of Hong Kong.” Property Management 19, no. 2 (May 1, 2001): 112–23. https://doi.org/10.1108/02637470110387830. Langstraat, Florian, and Rianne Van Melik. “Challenging the ‘End of Public Space’: A Comparative Analysis of Publicness in British and Dutch Urban Spaces.” Journal of Urban Design 18, no. 3 (August 2013): 429–48. https://doi.org/10.1080/13574809.2013.800451. Lau, Kwok-yu. Housing In the Other Hong Kong Report. Hong Kong: Chinese University Press, 1991. Marsillo, Laura, Nawapan Suntorachai, Keshava Narayan Karthikeyan, Nataliya Voinova, Lea Khairallah, and Angelos Chronis. “Context Decoder - Measuring Urban Quality through Artificial Intelligence,” 237–46. Ghent, Belgium, 2022. https://doi.org/10.52842/conf. ecaade.2022.2.237. Mehta, Vikas. “Evaluating Public Space.” Journal of Urban Design 19, no. 1 (January 1, 2014): 53–88. https://doi.org/10.1080/13574809.2013.854698.

Németh, Jeremy, and Stephan Schmidt. “Toward a Methodology for Measuring the Security of Publicly Accessible Spaces.” Journal of the American Planning Association 73, no. 3 (September 30, 2007): 283–97. https://doi.org/10.1080/01944360708977978. Ping Yan, Fung. “Public Housing in Hong Kong Past, Present and Future.” Chartered Institute of Housing Asian Pacific Branch, 2006. Sadler, Simon. Archigram: Architecture without Architecture. Cambridge, Mass: MIT Press, 2005. Sarkisian, Mark. Designing Tall Buildings: Structure as Architecture. New York, NY: Routledge, 2012. Seng, Eunice. “The City in a Building: A Brief Social History of Urban Hong Kong.” SITA 2017, no. 5 (2017). https://doi.org/10.54508/sITA.5.07. Shelton, Barrie, Justyna Karakiewicz, and Thomas Kvan. The Making of Hong Kong: From Vertical to Volumetric. London: Routledge, 2011. Smart, Alan. The Shek Kip Mei Myth: Squatters, Fires and Colonial Rule in Hong Kong, 1950 1963. Aberdeen, Hong Kong: Hong Kong Univ. Press, 2006. Schmidt III, Robert, and Simon Austin. Adaptable Architecture: Theory and Practice. Routledge, 2016. Smith, Constance, and Saffron Woodcraft. “Tower Block ‘Failures’?: High-Rise Anthropology.” Focaal 2020, no. 86 (2020): 1–10. https://doi.org/10.3167/fcl.2020.860101. Tang, Bo-sin, and Siu-wai Wong. “A Longitudinal Study of Open Space Zoning and Development in Hong Kong.” Landscape and Urban Planning 87, no. 4 (September 2008): 258–68. https://doi.org/10.1016/j.landurbplan.2008.06.009. Urban, Florian. Tower and Slab: Histories of Global Mass Housing. London: Routledge, 2012. Van Melik, Rianne, Irina Van Aalst, and Jan Van Weesep. “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space.” Journal of Urban Design 12, no. 1 (February 2007): 25–42. https://doi.org/10.1080/13574800601071170. Varna, George, and Steve Tiesdell. “Assessing the Publicness of Public Space:The Star Model of Publicness.” Journal of Urban Design 15, no. 4 (November 2010): 575–98. https://doi.or g/10.1080/13574809.2010.502350. Weintraub, Jeff Alan, and Krishan Kumar, eds. Public and Private in Thought and Practice: Perspectives on a Grand Dichotomy. Morality and Society. Chicago: University of Chicago Press, 1997. Xue, Charlie Q. L., and Kevin K. K. Manuel. “The Quest for Better Public Space: A Critical Review of Urban Hong Kong.” In Public Places in Asia Pacific Cities, edited by Pu Miao, 60:171–90. The GeoJournal Library. Dordrecht: Springer Netherlands, 2001. https://doi. org/10.1007/978-94-017-2815-7_9. Zamanifard, Hadi, Tooran Alizadeh, Caryl Bosman, and Eddo Coiacetto. “Measuring Experiential Qualities of Urban Public Spaces: Users’ Perspective.” Journal of Urban Design 24, no. 3 (May 4, 2019): 340–64. https://doi.org/10.1080/13574809.2018.1484664.

Bhagat | Pan | Wong

Németh, Jeremy, and Stephen Schmidt. “The Privatization of Public Space: Modeling and Measuring Publicness.” Environment and Planning B: Planning and Design 38, no. 1 (2011): 5–23. https://doi.org/10.1068/b36057.

03 Methodology

3.1 The Public-Private Evaluation Method 3.2 Tower Organization 3.3 Program Relationships 3.4 Fabrication and Material System 3.5 Analysis Tools

The P2 Tower

The Public-Private Evaluation Method Over time, as the sociability needs of people change, the form and functionality of the built space around them should change as well. In order to create such an adaptation system, it was first necessary to devise a systematic method to quantify a space’s sociability, namely the Sociability Spectrum. The team developed a series of parameters which constitute the sociability of a space along a spectrum, building upon existing models for measure publicness.

The team improved upon these models by directly address their shortcomings, ensuring each one was quantifiable, directly related to a space’s sociability, and existed within an architect’s domain. In doing so, the devised sociability evaluation method aimed to measure a space’s sociability such that this data can be utilized to inform the design and adaptation of an architectural artifact.

The Parameters and Sociability Calculation Method The parameters within the evaluation method existed in four dimensions: Ownership, Site Accessibility, Building Affordance, and Environment. Each category aimed to encompass one major portion of the architectural domain. The specific realm and definition of each dimension is as follows: Ownership: What is the legal status and program functionality of the building? Site Accessibility: How to occupants find, view, and enter the site? Building Affordance: How do occupants use, circulate, and occupy the building? Environment: What is the spatial quality of the building’s interior? Within each dimension, there existed a series of parameters which worked to quantify the relevant sociability metrics (Fig. 01). Each parameter was calculated in a quantifiable manner and incorporated domain boundaries which limited their scope to a relevant range. The resultant value was then remapped between 0 and 1 to normalize the value within an appropriate domain. Some parameters had embedded domains and others had manually constructed domains determined by laws, code requirements, or existing research in the field. Through this process, the resultant parameters were metrically comparable.

Once each individual parameter was calculated and normalized, the values were systemically combined to create one comprehensive value for a space’s sociability. To do this, each value was first summed within each dimension to create a combined score. Then, each combined score was weighted in accordance with its relevance to the sociability needs of the occupants. Finally, all weighted values were summed and remapped between 0 and 1 to achieve a single, inclusive value for the sociability of a space. The public-private evaluation method was used throughout the research as a tool to drive the design and adaptation of the tower morphology over time. As the sociability needs of the occupants changed, the design needs of the tower spaces changed, and the evaluation system was utilized to determine which changes were required.

PRIVATE

Visual Site Connections

OWNERSHIP

individual

Daylighting

Threshold Conditions

Ownership (Public/Private)

Access Points to the Site

architectural artifact

Density of People

Physical Accessibility Spatial Connectivity

SITE ACCESSIBILITY

Thermal Comfort

Spatial Proportions

quantiﬁable parameters

dimensions of publicness

BUILDING AFFORDANCE

Modes of Transit to the Site

Average Area Per Space Density of Function

Function (Public/Private)

Noise Protection

Centrality to Context Area of Outdoor Space

Use (Public/Private)

PUBLIC

ENVIRONMENT

Connectedness to Amenities

Area of Social Space

collective

Figure 13: Sociability Spectrum

DIMENSIONS

SITE ACCESSIBILITY How do people ﬁnd, enter, and view the site?

BUILDING AFFORDANCE How do people use, circulate, and occupy the building?

ENVIRONMENT What is the spatial quality of the building’s interior?

OWNERSHIP What is the legal status and programmatic function of the building?

Figure 14: Sociability Evaluation System

QUANTIFIED PARAMETERS

PARAMETER CAL

S.01 VISUAL SITE CONNECTIONS

0.32

S.02 ACCESS POINTS TO SITE

0.18

S.03 MODES OF TRANSIT TO SITE

0.40

S.04 CONNECTEDNESS TO AMENITIES

0.14

S.05 CENTRALITY TO CONTEXT

0.54

B.01 THRESHOLD CONDITION

0.23

B.02 OCCUPANT DENSITY

0.00

B.03 SPATIAL CONNECTIVITY

0.29

B.04 SPATIAL PROPORTIONS

0.00

B.05 AVERAGE AREA PER SPACE

0.00

B.06 FUNCTION DENSITY

0.07

B.07 PHYSICAL ACCESSIBILITY

0.06

B.08 AREA OF SOCIAL SPACE

0.11

B.09 AREA OF OUTDOOR SPACE

0.14

E.01 DAYLIGHTING

0.79

E.02 THERMAL COMFORT

0.45

E.03 NOISE CONDITION

0.03

B.01 OWNERSHIP

1.0

B.02 FUNCTION

0.0

B.03 PROGRAMMATIC USE

0.0

LCULATION

SUM = 1.58

WEIGHTING

FINAL RESULT

x 1.0 = 1.58

0.0 - 1.0 Private - Public SUM = 0.90

x 1.25 = 1.12 4.24

SUM = 1.27

x 1.0 = 1.29

SUM = 1.0

x 0.25 = 0.25

0.21

0.0 to 1.0 = Private to Public

OCCUPANT DENSITY

THRESHOLD CONDITION

How do people use, circulate and occupy the building?

BUILDING AFFORDANCE

ENTRANCE

B.03 Node Values / Nodes = 0.29 SPATIAL CONNECTIVITY

Analyzed Element Base Condition

APT A 5 PEOPLE APT B 7 PEOPLE

B.04 2.5m Room Height = 0.00

B.05 (430m * 18 Flrs)/ (40 Spaces * 18 Flrs) = 10m / Space = 0.00 AVERAGE AREA PER SPACE

SPATIAL PROPORTIONS

B.06 2 Functions / (40 Spaces * 18 Flrs) * 25 = 0.07 FUNCTION DENSITY

2.5m

LOBBY APARTMENT

B.07 (1 Accessible / 40 Spaces) * 2.5 = 0.06

B.08 50m Social Space / 430m = 0.11

PHYSICAL ACCESSIBILITY

AREA OF SOCIAL SPACE 2

B.09 1100m Site Area / (430m Building Area * 18 Flrs) = 0.14 AREA OF OUTDOOR SPACE

ACCESSIBLE SPACE NON-ACCESSIBLE SPACE

0.0 to 1.0 = Private to Public Analyzed Element

E.01

E.02 THERMAL COMFORT

DAYLIGHTING

OW.01

OWNERSHIP

1.0

Average Noise Absorption of Materials = 0.03

0.99

0.56

0.01

0.37

OW.02

OWNERSHIP

Public Ownership = 1.0

E.03 NOISE CONDITION

Average Yearly PMV = 0.45

Average Yearly PMV = 0.79

ENVIRONMENT

What is the spatial quality of the building’s interior?

Base Condition

What is the legal status and programmatic function of the building?

The P2 Tower

B.02 (430m * 18 Flrs) / (140 ppl * 18 Flrs) = 3.07sqm/pers. = 0.00

B.01 (1 Entrance / 430m Ground Floor) * 100 = 0.23

FUNCTION Private Function = 0.0

Public Ownership

OW.03

0.0 to 1.0 = Private to Public

USE

Analyzed Element

Private Use = 0.0

Base Condition

0.3

Public Function

Public Ownership Public Function Private Use

Private Function Private Use

Public Use

0.6

Public Ownership

0.0

Private Ownership Private Function Private Use

0.0 to 1.0 = Private to Public

Analyzed Element

S.01

73m Visible Boundary / 223m Site Boundary = 0.32

0.5 ACCESS POINTS TO SITE

(1 Access Point / 1100m Site) * 200 = 0.18 2

Bhagat | Pan | Wong

US DI RA

S.02

Base Condition

VISUAL SITE CONNECTIONS

How do people ﬁnd, enter and view the site?

S.03 S.04

POST OFFICE

20 Bus Stops, No Other Modes = 0.4

HOSPITAL

CONNECTEDNESS TO AMENITIES 1KM Min. Average Distance = 1296m = 0.14 BUS STOPS

S.05

CENTRALITY TO CONTEXT 2KM

RESTURAUNT

SIT EC O

Site Node Centrality Value = 0.54

PARK

T EX NT

SITE ACCESSIBILITY

SCHOOL

MODES OF TRANSIT TO SITE 1KM

SUPERMARKET

S.01 VISUAL ACCESS BANK

S.02 SITE ACCESS

LIBRARY

SCHOOL

100m

100

250m

0.0 to 1.0 = Private to Analyzed Element

ONNECTIONS

ry / 223m Site Boundary = 0.32

Base Condition

TS TO SITE

00m2 Site) * 200 = 0.18

2K M

US DI RA

ANSIT TO SITE 1KM

ther Modes = 0.4

SS TO AMENITIES 1KM

nce = 1296m = 0.14

O CONTEXT 2KM

y Value = 0.54

S.05 SITE CENTRALITY VALUE: 0.54

100

200

500m

Figure 15: Sociability Parameter Calculation Method

Tower Organization

The P2 Tower

The Principles of Bamboo Stems as a Structural System 1.0

0.9

0.7

0.6

0.5

0.4

Diaphragm

Cavity

Culm Wall

0.3

0.2

0.1

0.0

These principles of node distribution can be abstracted through mathematical equations to Mulyana et al. Bamboo Node Equation an architectural domain and+ serve the- basis -1.566x³ 1.8261x² +as 0.7468x 0.033 for a stable and materially efficient structural system of a tall tower. Empirical research by Mulyana et al. translated the node spacing Relative Internode Number (RIN) of various bamboo species into a third-order mathematical expression. 2 Through these equations, an initial guide for a tower design was achieved, where nodes translated to major horizontal structure such as floor systems, culm walls became major vertical structure, and internodes became large, segmented spatial zones. 0.1

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In addition to its structural capabilities, the organization strategy of this biological system affords a tall tower the ability to adapt and reconfigure, because all of the major structure lies on the perimeter of the form, providing free interior spans. Additionally, the optimized material usage and geometry in bamboo stems minimizes the area and locations of fixed structural elements in the proposed system, while maintaining maximum structural capacity. Such an organization strategy provides the freedom and flexibility to employ an adaptable architectural system.

Bamboo Stem Cross Section

Figure 16: Bamboo Stem Elements

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The bamboo stem’s internal organization has evolved over time to create a highly efficient structural system for resisting bending, buckling, and uplifts. In particular, the spacing of nodes and internodes are mathematically arranged and proportioned in accordance with their location along the entire stem, where the base employs a denser spacing and thicker node to resist high lateral loads and the upper portions sequentially decrease in size as the loads decrease vertically to minimize weight and material.

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Figure 17: Mathematical Expression of Bamboo Nodes

Mark Sarkisian et al., “Organic and Natural Forms in Building Design,” 2010: 4. https://www.researchgate.net/ publication/328782547_Organic_and_Natural_Forms_in_Building_Design. 2 Mulyana, B., and R. Reorita. “Mathematical Expression of Internode Characteristics of Yellow Ampel Bamboo (‘Bambusa Vulgaris’ Var. Striata).” Series II: Forestry Wood Industry Agricultural Food Engineering, June 28, 2022, 43–56. https://doi.org/10.31926/ but.fwiafe.2022.15.64.1.4. 1

Co-Evolutionary Algorithms for Private-Public Distribution

Yet, these algorithms break down under particular environmental conditions. Firstly, EAs find difficulty in cases of extremely large search spaces. Additionally, the absence of inherent, objective procedures for quantifying an individual’s fitness greatly limits the outcomes body plan gene

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Figure 18: Evolutionary Algorithm Workflow

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Figure 19: Co-Evolutionary Algorithm Workflow

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Charles Darwin’s Theory of Evolution introduced the notion that through natural selection, populations in nature will adapt over time in response to specific environmental conditions. Such a notion inspired the development of evolutionary algorithms (EA), which computationally mimic this process by ‘evolving’ a population over time based upon a series of fitness criteria. Architecturally, an EA provides an efficient methodology for reconciling the complexity of numerous design factors.

of EAs. Lastly, EAs struggle to optimize when the complexity of the search space exceeds a limit of rationality. In such cases, coevolutionary algorithms (CoEA) off a potential solution to these limitations by decomposing a complex and high-dimensional problem into simpler parts. In nature, coevolution refers to the evolution of “two major groups of organisms with a close and evident ecological relationship.” Translating such a notion into a computational framework, a CoEA evolves two or more interconnected populations in tandem such that the evolutionary growth of one population influences the other to adapt, and vice-versa. A CoEA differs from a typical EA in that the fitness of any individual is subjective. The algorithm is less concerned with any one individual but instead, the interactions of an individual with an individual of the other population. These interactions can be cooperative or competitive. Such a system uniquely situates these individuals within a specific environment of quantified relationships.

The P2 Tower

Program Relationships

Figure 20: Small-World Network

Small-world Network as a Spatial Relationship System In the real world, social networks and brain neuron networks efficiently accomplish the transfer of information, exhibiting the qualities of small-world networks (SWN). A SWN exhibits properties of high clustering and low path length between nodes. These properties make node-to-node connections more efficient in the system, seeing as the short average path length allows for fast information dissemination between nodes and the high clustering ensures that points are quickly connected in their localized zones. These principles can be abstracted to architecture as spatial relationships throughout the horizontal and vertical planes of an architectural system. SWN can simulate the connections between spaces, where the nodes behave as abstracted locations of different spaces or functions and the network connections act as the relationships between these programs. Thus, the node relationships and connection logics of a SWN offer a highly efficient methodology

for interweaving public and private spaces throughout a tall building, strengthening their interaction and cooperation. Additionally, such a system is highly adaptable, enabling the tower to easily shift these programmatic relationships as the sociability of the people change seeing as it is a robust network with safeguards for random failures of nodes and connections. Even if some nodes or connections fail or disappear, the network still remains connected, and paths will persist to other nodes in the network, providing a flexible system for an adaptable architecture.

Figure 21: Small-World Network Equations

Qawi K. Telesford et al., ‘The Ubiquity of Small-World Networks’, Brain Connectivity 1, no. 5 (2011): 367–75, https://doi. org/10.1089/brain.2011.0038. 8 Duncan J. Watts and Steven H. Strogatz, ‘Collective Dynamics of “Small-World” Networks’, Nature 393, no. 6684 (June 1998): 440–42, https://doi.org/10.1038/30918. 9 Duncan S. Callaway et al., ‘Network Robustness and Fragility: Percolation on Random Graphs’, Physical Review Letters 85, no. 25 (18 December 2000): 5468–71, https://doi.org/10.1103/PhysRevLett.85.5468. 7

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SEGMENT 05 vertical connection SEGMENT 04 vertical connection SEGMENT 03 vertical connection SEGMENT 02 vertical connection SEGMENT 01

TOPOLOGICAL RELATIONSHIPS

Figure 22: Small-World Network in Architecture

ARCHITECTURAL TRANSLATION

The P2 Tower

Fabrication and Material System Rice Husk

+ Robotic 3D Printing

Recycle Aggregate

Concrete Material Natural Fiber Reinforcements

Figure 23: Fabrication System

Additive Manufacturing: Robotic 3D Printing Additive manufacturing is a process where material is deposited layer by layer to create a given object or form.10 Robotic 3D printing is situated within this broad category, defining a more specific manufacturing process which utilizes a 6-axis robotic arm to maneuver space and integrates an end effector tool to deposit material in layers.11 Such a process allows for the creation of bespoke morphologies, which are often difficult to hand craft, and minimizes material wastage. The robotic arm itself also affords the ability to move through space in

all six axes and print with a wide variety of materials systems, providing a higher degree of customizability and range of form capabilities.12 These advantages proved highly pertinent for an adaptable building system. Robotic 3D printing can seamlessly manufacture the bespoke geometries from the research without the need for hundreds of unique formworks or jigs, significantly reducing the time, material, and manpower for fabrication. Therefore, the research explored the possibilities of robotic 3D printing within its range of limitations to maximize its potential in the context of an adaptable architecture.

Rebecca Linke, “Additive Manufacturing, Explained | MIT Sloan,” MIT Sloan, December 7, 2017, https://mitsloan.mit.edu/ideasmade-to-matter/additive-manufacturing-explained. 11 “Automation and Additive Manufacturing,” KUKA AG, accessed June 29, 2023, https://www.kuka.com/en-gb/products/processtechnologies/3d-printing. 12 Linke, “Additive Manufacturing, Explained | MIT Sloan.” 13 H. Tian and Y. X. Zhang, “Tensile Behaviour of a Sustainable Fibre Reinforced Cementitious Composite under Different Strain Rates,” in Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), ed. Lin Ye (Oxford: Woodhead Publishing, 2014), 316–20, https://doi.org/10.1533/9780081002254.316. 10

Concrete is one of the few materials that can be used to 3D print structurally stable architectural components at a large scale, due to its high flow state and consistency when printing and its high structural capacity when fully hardened. However, concrete is also a highly unsustainable material. Thus, there has been a recent shift towards creating new mixtures of concrete with less embodied carbon. Fiber-reinforced cementitious composites are one potential

CO2 Sources

solution, where a portion of cement is replaced by another low carbon material such as fly ash. These composites not only reduce the embodied carbon of the material system but are also shown to improve upon the ductility of standard concrete mixtures due to the integration of fiber elements.13 Additionally, these materials are obtainable from local contexts, further decreasing the carbon related to transportation. Thus, this research explored the use of these composites as the material system for the adaptable components. Specifically, the thesis utilized a cementitious composite of rice husk and recycled aggregate, which are local to Hong Kong.

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Figure 25: Fiber-Reinforced Cementitious Composites Lifecycle

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Material Systems: Fiber-Reinforced Cementitious Composites

The P2 Tower

Material Systems: Bamboo Strip Weaving as Rebar Reinforcement and Formwork Rebar reinforcement and formwork can be integrated into concrete 3D printing to extend the range of structural capabilities and morphologies that are possible to fabricate, but rebar itself also has a high embodied carbon. Bamboo strip weaving offers a low-carbon alternative to rebar that can act as integrated formwork and reinforcement. Bamboo strip weaving is a traditional Chinese artform which utilizes thin strips of bamboo to achieve self-

standing morphologies without the need for additional joinery or attachment systems. Particularly, the Kagome weave is a triaxial pattern which can produce highly complex three-dimensional surfaces due to its selfbracing capacity and high shear resistance.14 Additionally, it enables a high degree of geometrical control, high redundancy, and local reparability, allowing designers to generate and fabricate a wider range of morphologies using this technique.15 Thus, combining woven bamboo with concrete 3D printing both reaches the necessary structural performance of large scale forms and increases the range of achievable morphologies.

Figure 26: Bamboo Growth Regions

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Phil Ayres, Alison Grace Martin, and Mateusz Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” n.d., 75. 15 Ayres, Martin, and Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.”, 75. 14

Figure 28: Bamboo Weaving

The P2 Tower

Analysis Tools Finite Element Analysis (FEA) Finite Element Analysis (FEA) is used to evaluate the structural performance of a digital model by subdividing the input geometry into simplified, discrete elements and applying loads to these simplified elements through the use of a physics engine and mathematical calculations in order to approximate the structural performance of the design.16 FEA specifically provides numerical data and digital visualizations on a model’s deformation, mechanical stresses, and utilization, among others.17 Karamba3D was used as the FEA software to evaluate and compare the structural performance of design candidates. Its ability to seamlessly integrate with Grasshopper enabled the design process to maintain a continuous feedback loop with other Grasshopper-based analysis software as different design options were evaluated, enabling a holistically informed design decision.

Computational Fluid Dynamics (CFD) Computational Fluid Dynamics (CFD) is the numerical modeling of fluid behavior, typically wind or water, around and within an object through mathematical equations and analytical techniques.18 To conduct this analysis, fluid particles are generated at one end of the determined field and are then continuously recalculated and tracked over a given number of iterations throughout the simulation process. Computational Fluid Dynamics enables designers to properly understand fluid patterns and movements as critical data during the design process.

The research utilized Ladybug Tool’s CFD plugin for Grasshopper, Dragonfly, to predict wind pressure loads on the building, which was critically important due to the context of Hong Kong and the variable and high wind loads present on tall building for the design of the structural system. Additionally, since the tower morphology adapted over time, it was important to continuously reevaluate the tower’s reaction to wind flows and forces at each iteration.

Artificial Neural Network (ANN) An artificial neural network (ANN) is a machine learning model whose principles are extracted from biological neurons in the brain. It consists of three main layers of neurons: the input layer, multiple hidden layers, and the output layer.19 Information is passed forward through each layer, where each neuron is connected to one another by an associate weight and threshold value. By continuously activating and deactivating different combinations of neurons, the model is trained to predict output values more accurately. The research trained an ANN using the plugin LunchboxML for Grasshopper to predict the wind pressure on a building for any tower morphology, site context, and wind conditions. The use of an ANN afforded the workflow a high degree of flexibility and applicability for new and changing scenarios.

“Introduction to Finite Element Analysis,” Introduction to finite element analysis, accessed June 29, 2023, https://www.open.edu/ openlearn/science-maths-technology/introduction-finite-element-analysis/science-maths-technology/introduction-finite-elementanalysis. 17 “Finite Element Analysis Software | Autodesk,” accessed June 29, 2023, https://www.autodesk.co.uk/solutions/finite-elementanalysis. 18 H. Lomax, Thomas H. Pulliam, and David W. Zingg, “Introduction,” in Fundamentals of Computational Fluid Dynamics, ed. H. Lomax, Thomas H. Pulliam, and David W. Zingg, Scientific Computation (Berlin, Heidelberg: Springer, 2001), 1–5, https://doi. org/10.1007/978-3-662-04654-8_1. 19 MIT News | Massachusetts Institute of Technology. “Explained: Neural Networks,” April 14, 2017. https://news.mit.edu/2017/ explained-neural-networks-deep-learning-0414. 16

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Figure 29: Artificial Neural Network (ANN)

The P2 Tower

Bibliography Ayres, Phil, Alison Grace Martin, and Mateusz Zwierzycki. “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” n.d. Ehrich, Paul and Peter Raven. “Butterflies and Plants: A Study in Coevolution.” Evolution 18, no. 4 (1964): 586-608. https://doi.org/10.2307/2406212 “Finite Element Analysis Software | Autodesk.” Accessed June 29, 2023. https://www.autodesk. co.uk/solutions/finite-element-analysis. Heschong, Lisa, and Kevin Van Den Wymelenberg. “IES Spatial Daylight Autonomy (SDA) and Annual Sunlight Exposure (ASE).” Illuminating Engineers Society, 2022. Introduction to finite element analysis. “Introduction to Finite Element Analysis.” Accessed June 29, 2023. https://www.open.edu/openlearn/science-maths-technology/introduction-finiteelement-analysis/science-maths-technology/introduction-finite-element-analysis. Janssen, Jules J. A. Mechanical Properties of Bamboo. Vol. 37. Forestry Sciences. Dordrecht: Springer Netherlands, 1991. https://doi.org/10.1007/978-94-011-3236-7. KUKA AG. “Automation and Additive Manufacturing.” Accessed June 29, 2023. https://www. kuka.com/en-gb/products/process-technologies/3d-printing. Linke, Rebecca. “Additive Manufacturing, Explained | MIT Sloan.” MIT Sloan, December 7, 2017. https://mitsloan.mit.edu/ideas-made-to-matter/additive-manufacturing-explained. Lomax, H., Thomas H. Pulliam, and David W. Zingg. “Introduction.” In Fundamentals of Computational Fluid Dynamics, edited by H. Lomax, Thomas H. Pulliam, and David W. Zingg, 1–5. Scientific Computation. Berlin, Heidelberg: Springer, 2001. https://doi. org/10.1007/978-3-662-04654-8_1. MIT News | Massachusetts Institute of Technology. “Explained: Neural Networks,” April 14, 2017. https://news.mit.edu/2017/explained-neural-networks-deep-learning-0414. Oldroyd, David R. “Charles Darwin’s Theory of Evolution: A Review of Our Present Understanding.” Biology and Philosophy 1, no. 2 (June 1, 1986): 133–68. https://doi. org/10.1007/BF00142899. Potter, Mitchell A., and Kenneth A. De Jong. “Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents.” Evolutionary Computation 8, no. 1 (March 2000): 1–29. https://doi.org/10.1162/106365600568086. Sarkisian, Mark, P Lee, E Long, and David Shook. “Organic and Natural Forms in Building Design,” 2010. https://www.researchgate.net/publication/328782547_Organic_and_ Natural_Forms_in_Building_Design. Showkatbakhsh, Milad, and Mohammed Makki. “Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution.” Buildings 12, no. 9 (September 17, 2022): 1473. https://doi.org/10.3390/buildings12091473. Tian, H., and Y. X. Zhang. “Tensile Behaviour of a Sustainable Fibre Reinforced Cementitious Composite under Different Strain Rates.” In Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), edited by Lin Ye, 316–20. Oxford: Woodhead Publishing, 2014. https://doi.org/10.1533/9780081002254.316. Vellei, Marika, Richard de Dear, Christian Inard, and Ollie Jay. “Dynamic Thermal Perception: A Review and Agenda for Future Experimental Research.” Building and Environment 205 (November 1, 2021): 108269. https://doi.org/10.1016/j.buildenv.2021.108269.

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04 Research Development

4.1 Structural System Experiments 4.2 Private-Public Distribution Experiments 4.3 Programmatic Topology Experiments 4.4 Material Fabrication System Experiments

The P2 Tower

TOWER MORPHOLOGY

Project Workflow

STRUCTURAL SYSTEM

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The P2 Tower

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Figure 30: Scope of Research Development Phase

Overview The design of the P2 Tower was subdivided into six major sections: the tower morphology, structural system, public-private distribution, programmatic topology, space organization,

and material fabrication system. To successfully achieve all areas, the more complex sections were broken into smaller, more simplified experiments to test their functionalities. These initial studies provided a foundational understanding of each section, facilitating their unification into a full tower design in the Design Development and Design Proposal phases.

4.1 Structural System Studies the Design Development phase to formulate the tower morphology and structural system. The bamboo stem node equation determined the spacing of major structural tower segments and the ANN predicted wind loads on the tower to perform structural analysis.

4.1.1 Bamboo Internode Mathematical Expression Scaling Experiment Experiment Description: The mathematical spacing of the internodes along a bamboo stem were quantified by various researchers through empirical studies and regression models, but it is naïve to assume such equations are scalable to a tall tower and elicit the same structural behaviors. Therefore, the experiment aimed to map these mathematical expressions to the scale of a tall tower.

Experiment Set-up: The experiment applied the following mathematical expression from Mulyana et al. to establish internodal, lateral bracing of a tall tower with a square footprint measuring 10m x 10m.1 RIL = 2.8312(RIN)3 - 8.926(RIN)2 + 5.2101(RIN) - 0.0062

RIL = Relative Internode Length RIN = Relative Internode Number In addition to the lateral bracing, the tower was equipped with cross-bracing system between internodes. The lateral bracing had a steel crosssection diameter of 75cm and a thickness of 5cm while the cross-bracing had a steel cross-section diameter of 50cm and a thickness of 3cm. FEA using Karamba3D was employed to calculate the maximum deformation of the structure under an eastward wind load of 943 kN which

ax³ + bx² + cx + d a b c d

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[-2.066, -1.066] [1.3261, 2.3261] [0.2468, 1.2468] [-0.533, 0.467]

Figure 31: Internode Equation Experiment Setup

Mulyana, B., and R. Reorita. “Mathematical Expression of Internode Characteristics of Yellow Ampel Bamboo (‘Bambusa Vulgaris’ Var. Striata).” Series II: Forestry Wood Industry Agricultural Food Engineering, June 28, 2022, 43–56. https://doi.org/10.31926/ but.fwiafe.2022.15.64.1.4.

Bhagat | Pan | Wong

The initial experiments surrounding the structural system studied the effects of wind, a crucial aspect of tall tower design. One experiment studied the use of bamboo stem internode placements at the scale of a tower. The second experiment developed an ANN to predict wind loads on the tower’s structural system. Both experiments were utilized during

The P2 Tower

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scaled up to 2017 kN along the vertical height of the structure. The structure had fixed supports in its four corners vertices on the ground. Then, a single-objective optimization was conducted utilizing Wallacei with default algorithm parameters to optimize the equation to provide minimized deformation for different numbers of internodes ranging from 5 to 9 and varying heights from 100m to 150m. The equation was abstracted as follows with the coefficients of the third-order equation acting as genes with

ranges of plus and minus 0.5 from the original equation. Experiment Results: The experiment found that the translated equation for using bamboo internode placement principles at a tower scale is: -1.566x3 + 1.8261x2 + 0.7468x -0.033. Through post-analysis, it was shown that the segment distribution generated by this equation performed better than the original equation, particularly in situations with less structure.

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Figure 33: Internode Equation Experiment Post-analysis

Bhagat | Pan | Wong

Scaled Equation

The P2 Tower

4.2 Computational Fluid Dynamics Neural Network Experiment

single-objective optimization was conducted using Wallacei with the default algorithmic parameters to minimize the error of the neural network.

Experiment Description: Since the proposed tower workflow is applicable to multiple locations and CFD is highly time intensive and computationally heavy, the experiment aimed to introduce variable site flexibility by training an ANN to accurately predict the wind pressure for any given tower morphology.

Neural Network Validation: The trained ANN was post-analyzed for accuracy and performance using 30% of the original data set as validation, which was not utilized for training. From these predicted wind pressure values, the percentage error was calculated and averaged across all the nodes on the tower to estimate the difference. From these predicted wind pressure values, the percentage error was calculated and averaged across the entire data set.

Neural Network Training: The experiment utilized the tower morphologies created in Experiment 4.1 to generate the training data set for the ANN. The training input data for the ANN consisted of the deconstructed xyzcoordinate of the node point on the tower, the deconstructed normal vector of the surface at the node point, the wind speed (m/s), and the proximity count of the node to other nodes within a 5m radius. From these inputs, the training output data for the ANN was the wind pressure (kN) on the tower at the node. On any given tower morphology, CFD analysis using Butterfly was conducted to calculate the wind pressure (kN) at the nodes along the tower. The CFD utilized wind speeds ranging from 5 m/s to 15 m/s, a mesh resolution of 3.0, and ran for 200 iterations. 24 random tower morphologies were tested, generating a training set with over 500,000 inputs. Lastly, another

Experiment Results: The experiment successfully created an ANN based on similar tower morphologies in various site conditions. Upon validation, it was shown to achieve an average percent error around 50%, but when this was corrected for outlying data point, the error dropped to 10-15% on average. Further research should examine whether such a training set was sufficient to accurately substitute for conducting a CFD and re-evaluate how to select a diverse range of towers for the training set.

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Figure 35: Wind Pressure ANN Setup

The P2 Tower

4.2 Public-Private Distribution Studies The initial experiments surrounding the public-private distribution in the tower studied co-evolutionary principles. Since the tower integrated both public and private programs, it was necessary to explore co-evolutionary algorithms as a means to evolve both spaces simultaneously and meet their specific objectives. Three types of co-evolutionary algorithms were studied: parasitism, commensalism, and

mutualism. These methods were explored using a simple scenario of two towers sharing the same site to understand the functionality of the algorithm more clearly. Their advantages and disadvantages were noted, and one method was selected for use. The selected coevolution method was utilized during the Design Development phase to simultaneously grow the public and private spaces in the tower.

4.2.1 Co-Evolutionary Algorithm Experiments

consisted of two towers sharing the same site which evolved simultaneously. (T1 and T2) Each tower was divided into four quadrants and a series of genes controlled the offset distance from the site boundary, the height of each tower quadrant, the rotation of the tower, the quadrant division locations, and the ratio of the site relegated to each tower. Before each CoEA experiment was conducted, each tower was individually optimized using a tradition EA in order to identify the optimal gene ranges for each tower. The conducted CoEA utilized these optimized gene ranges in its simulation. In doing so, the optimization focused more on the relationship between the fitness objective as opposed to each individual one.

Experiment Description: These experiments examined the advantages and disadvantages of co-evolutionary algorithms in simple, architectural scenarios. Experiment Set-up: Each exploratory experiment conducted a multi-objective optimization using Wallacei with default algorithm parameters on the same primitive but different fitness objectives to simulate three types of co-evolution found in nature: parasitism, commensalism, and mutualism. The primitive

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Figure 36: Three Types of Co-Evolution

Ideal-Team Solution

T1 EA Optimization Phenotypes

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T2 EA Optimization Phenotypes

T1T2 CoEA w/ Optimized Gene Ranges Phenotypes

Figure 37: EA and CoEA Phenotype Comparison

The P2 Tower

4.2.1.1 Paracitism Co-Evolutionary Experiment Experiment Set-up: Using the two-tower primitive, each tower evolved towards conflicting fitness objectives. T1 optimized for maximized daylighting and maximized height difference between quadrants, while T2 optimized for minimized solar radiation and maximized floorto-area ratio. Experiment Results: The results of the experiment showed that T1 optimized well,

T1 EA Optimization

T2 EA Optimization

FC1 | Maximized Daylighting FC1 Range: 0.010 To 0.333 Δ = 0.323

FC2 | Maximized Tower Height Difference FC2 Range: 2.532e-7 To 2.997e-7 Δ = 4.642e-8

and T2 tower failed to optimize at all. Upon comparison to the optimization of each tower individually through a traditional EA, T1 optimized to a similar degree as it had individually while T2 was unable to achieve even a remotely similar level of optimization. Such results, while not necessarily ideal in certain scenarios, provided an insight into how the design of a single architectural artifact in more complex design challenges may adversely affect its neighbors, showcasing a ‘singleoptimized solution’.

T1T2 CoEA w/ Optimized Gene Ranges

T1T2 CoEA w/o Optimized Gene Ranges

FC1 | Maximized Daylighting

FC1 Range: 0.011 To 1 Δ = 0.988 (+305.99%)

FC1 Range: 0.011 To 1 Δ = 0.988 (+305.91%)

FC2 | Maximized Tower Height Difference

FC2 Range: 2.854e-7 To 6.398e-7

FC2 Range: 3.073e-7 To 1.809e-6

Δ = 3.544e-7 (+763.65%)

FC3 | Minimized Solar Radiation FC3 Range: 83564.656 To 349508.827 Δ = 265944.170

FC4 | Maximized Floor-to-Area Ratio FC4 Range: 0.2283 To 2.285 Δ = 2.057

Δ = 1.502e-6 (+3236.53%)

FC3 | Minimized Solar Radiation

FC3 Range: 56751.533 To 335171.650 Δ = 278420.116 (+104.69%)

FC3 Range: 51691.539 To 370598.854 Δ = 318907.314 (+119.91%)

FC4 | Maximized Floor-to-Area Ratio

FC4 Range: 0.231 To 3.438

Δ = 3.20613 (+155.81%)

Figure 38: Paracitism CoEA Results

FC4 Range: 0.242 To 5.649

Δ = 5.407 (+262.81%)

4.2.1.2 Commenselism Co-Evolutionary Experiment

T1 EA Optimization

T2 EA Optimization

FC1 | Minimized Solar Radiation FC1 Range: 29817.880 To 219798.379 Δ = 189989.499

FC2 | Maximized Site Shading

T1T2 CoEA w/ Optimized Gene Ranges

T1T2 CoEA w/o Optimized Gene Ranges

FC1 | Minimized Solar Radiation

FC1 Range: 19871.868 To 73514.449 Δ = 53642.581 (-28.23%)

FC1 Range: 33405.885 To 232178.578 Δ = 198772.692 (104.62%)

FC2 | Maximized Site Shading

FC2 Range: 338244 To 880920

FC2 Range: 104079 To 357270 Δ = 253191

Δ = 542676 (+214.33%)

FC3 | Maximized Average Height FC3 Range: 0.02 To 0.046 Δ = 0.026

FC4 | Maximized SA:V Ratio FC4 Range: 0.214 To 0.460 Δ = 0.246

FC3 | Maximized Average Height FC3 Range: 0.019 To 0.020 Δ = 0.001 (-3.84%)

FC4 | Maximized SA:V Ratio FC4 Range: 0.159648 To 0.241735 Δ = 0.082 (-33.33%)

Figure 39: Commensalism CoEA Results

FC2 Range: 414937 To 1468213

Δ = 1053276 (416.00%)

FC3 | Maximized Average Height FC3 Range: 0.020 To 0.046 Δ = 0.02 (+98.34%)

FC4 | Maximized SA:V Ratio FC4 Range: 0.214 To 0.497

Δ = 0.282 (+114.97%)

67 Bhagat | Pan | Wong

Experiment Set-up: Using the two-tower primitive, the fitness objectives of T2 benefited those of T1 but not reversely. T1 optimized for minimized solar radiation and maximized site shading, while T2 optimized for maximized average height and maximized surface area-tovolume ratio.

Experiment Results: The results of the experiment showed that T1 optimized well, while T2 optimized moderately. Upon comparison to the optimization of each tower individually through a traditional EA, T1 optimized to a similar degree as it had individually while T2 optimization did not achieve the same degree of convergence and demonstrated a broader range of performance values.

The P2 Tower

4.2.1.3 Mutualism Co-Evolutionary Experiment Experiment Set-up: Using the two-tower primitive, each tower evolved towards fitness objectives which benefited one another. T1 optimized for minimized solar radiation and maximized site shading, while T2 optimized for maximized open space and maximized daylighting. Experiment Results: The results of the experiment showed that each tower optimized

T1 EA Optimization

T2 EA Optimization

FC1 | Minimized Solar Radiation FC1 Range: 29817.880 To 219798.379 Δ = 189989.499

FC2 | Maximized Site Shading FC2 Range: 104079 To 357270

for their individual fitness objectives moderately. Upon comparison to the optimization of each tower individually through a traditional EA, the optimization did not achieve the same degree of convergence and the performance ranges were much broader. Yet, such results demonstrated an ‘ideal-team solution’ scenario where the two optimized towers represent a balance between the morphological ideals of one tower and that of the other, highlighting how a design problem may be formulated to benefit more than one interested party.

T1T2 CoEA w/ Optimized Gene Ranges

T1T2 CoEA w/o Optimized Gene Ranges

FC1 | Minimized Solar Radiation

FC1 Range: 25664.667 To 86896.257 Δ = 61231.590074 (-32.22%)

FC1 Range: 45672.748 To 241890.065 Δ = 196217.316 (103.27%)

FC2 | Maximized Site Shading

FC2 Range: 306454 To 560282

Δ = 253191

Δ =253828 (+100.25%)

FC3 | Maximized Open Space

FC2 Range: 155575 To 544443

Δ = 388868 (153.58%)

FC3 | Maximized Open Space

FC3 Range: 0.0237 To 0.0531 Δ = 0.029

FC3 Range: 0.0232 To 0.0335 Δ = 0.0103 (-35.51%)

FC3 Range: 0.0236 To 0.0542 Δ = 0.0306 (+105.51%)

FC4 | Maximized Daylighting

FC4 Range: 7.798e-7 To 2.934e-6

FC4 Range:8.204e-7 To 5.275e-6

FC4 Range: 7.526e-7 To 3.292e-6 Δ = 2.539e-6

Δ = 2.155e-6 (-84.87%)

Figure 40: Mutualism CoEA Results

Δ = 4.4545e-6 (+175.44%)

Co-Evolution Experiment Results

Based upon these results, the research moved forward with the mutualism CoEA in

Upon reflection, traditional analysis methods, such as standard deviation graphs and parallel coordinates plot, do no properly reflect the performance of the CoEA in that the relationships are obsercured. Further research should refine the methodology for analyzing the performance relationship between the two evolving populations in order to understand the proper effectiveness of the CoEA.

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Experiment Results: The exploratory CoEA experiments demonstrated a shift in the optimization results from traditional EAs in that the optimized phenotypes and their respective performances are related interrelated. Such results provided different benefits depending on the original design objectives such as a prioritization of one population or an assisted evolution.

Experiment 5.1 to simultaneously evolve the public and private distributions throughout the tower.

4.3 Program Topology Studies

The P2 Tower

The initial experiments surrounding the programmatic topology focus on topological relationships to situate programs within the tower based on their degree of sociability. This was achieved by using the small world network algorithm, which created an efficient network between a series of nodes. In the tower design, each node related to a program, such as an education center, food hub, or working

4.3.1 Small World Network Experiments Experiment Description: The SWN created connections between a series of weighted nodes to create appropriate pathways between programs in the tower design. However, since the SWN is inherently random, an EA was required to obtain the desired objectives. Experiment Set-up: This experiment created a logic of connectivity between architectural functions to achieve a well-connected, yet efficient, network. The network was controlled through the following genes: the radius of connectivity with other points, the number of connections to other points, and the rate of reduction for connections. Connection rules

Random E F

space. Each node was also specifically weighted to favor certain connections over others, where public spaces were weighted more heavily than private ones to ensure a gradient of sociability throughout the tower. The topological relationship workflow developed during this experiment were used in the Design Development phase to create program networks for the tower design.

were integrated within the small world network to facilitate network creation. These genes were manipulated to achieve a maximized clustering of points, a minimized path count, a maximized path weighting, and a node weighting closest to the required program sociability score. Experiment Results: This experiment showcased the SWN’s ability to create highly efficient topological relationships when optimized through an EA. By modifying the base conditions and weights, designers easily obtain the desired program relationships which are efficient, diversified, and interconnected. The generated connections also embedded a level of redundancy in the pathways, which is ideal for an adaptable tower system.

Regular

Small-world E

F C

A I

A I O J

O J

N K

A I

O J

N K L

Increasing randomness

Figure 41: Small World Network Concept

N K L

INPUT INFORMATION

TOWER MORPHOLOGY

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PUBLIC-PRIVATE SEGMENTS

C G B H A I

C(i) = E(i) / T(i)

J N K

g1 | Distance Between Points

FC01 | Maximized Cluster in Network

A J

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FC02 | Minimized Path Count

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g3 | Random Connection with Other Points

SPATIAL ORGANIZATION

Figure 42: Small World Network Evolutionary Algorithm Set-up

FC03 | Maximized Path Weight

3 2.05

5.02

3.1

2.85

FC04 | Minimized Difference Between Weight and Required Wieght

The P2 Tower

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-12507683 311976073

11579219

5899084

3957667

2977694

2386711

1991465

1708528

1495986

1330474

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Figure 43: Small World Network Evolutionary Algorithm Results

0.762

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0.397

0.342

0.301

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FC2 | Min Path Count

0.22

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0.187

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-79.5

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0.57

FC4 | Min Differences Between Weight

0.498

4.4 Material Fabrication Variable Control Studies The initial experiments surrounding the material fabrication system focused on controlling the parameters for bamboo weaving, including polygon Gaussian curvature, strip width to depth ratio, weave density for 3D printing, and the joint system. The data from these

tests helped create a computational workflow which replicated the bamboo’s bending behavior. These initial experiments were used in the Design Development phase to create the weaving pattern for the component design.

0.006 GAUSSIAN CURVATURE

The P2 Tower

0.003 SYNCLASTIC

0.000

ANTICLASTIC

-0.003 -0.006 -0.010 4

NUMBER OF SIDES Figure 44: Polygon Gaussian Curvature: Experiment Results

4.4.1 Polygon Gaussian Curvature Experiment Description: This experiment determined how the introduction of different polygons affected the local Gaussian curvature of a woven artifact. Experiment Set-up: Four to nine sided polygons were tested, and all samples maintained a 6mm strip width, 40cm strip length, and 8mm strip thickness. Once woven, these artifacts were 3D scanned and recreated digitally to obtain the Gaussian curvature at the polygon location.

Experiment Results: The team found polygons with less than six edges produced a synclastic curvature, while polygons with more than six edges produced an anticlastic curvature. As polygon edge count increased or decreased towards nine or four sides respectively, the values of this curvature increased, causing a more drastic curvature. Additionally, it was found weaving an artifact with polygon edge counts of lower than four or higher than nine were challenging, demarcating the domain of the achievable curvatures. The curvature data and domain informed the locations where the computational system induces specific polygon geometries.

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SYNCLASTIC CURVATURE

Four Sided Polygon

Five Sided Polygon

Gaussian Curvature: 0.0067

Gaussian Curvature: 0.00134

NO CURVATURE

ANTICLASTIC CURVATURE

Six Sided Polygon

Seven Sided Polygon

Gaussian Curvature: 0.0

Gaussian Curvature: -0.00132

ANTICLASTIC CURVATURE

Eight Sided Polygon

Nine Sided Polygon

Gaussian Curvature: -0.005

Gaussian Curvature: -0.0103

Figure 45: Polygon Gaussian Curvature: Woven Samples

DEVIA GAU

pth Ratio: 12.5:1 om Digital: 13mm

+0.001 +0.002

2.6 : 1

4.6 : 1 5 : 1

6.5 : 1

12.5 : 1

DEVIATION FROM DIGITAL MODEL (mm)

60mm 40mm

ACCEPTABLE WIDTH / DEPTH RATIOS

20mm 0mm -20mm

TARGET DEVIATION

-40mm 2.6 : 1

pth Ratio: 6.5:1 om Digital: 15mm

4.6 : 1 5 : 1

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WIDTH / DEPTH RATIO Target Curvature Actual Curvature DEVIATION FROM TARGET GAUSSIAN CURVATURE

m Width

pth Ratio: 12.5:1 om Digital: 13mm

8.75 : 1

WIDTH / DEPTH RATIO

m Width The P2 Tower

TARGET CURVATURE

-0.003 -0.002

ACCEPTABLE WIDTH / DEPTH RATIOS

-0.001 0.000 +0.001

TARGET CURVATURE

+0.002 2.6 : 1

4.6 : 1 5 : 1

6.5 : 1

8.75 : 1

12.5 : 1

WIDTH / DEPTH RATIO

m Width DEVIATION FROM DIGITAL MODEL (mm)

60mm Figure 46: Strip Width to Depth Ratio: Experiment Results

40mm 20mm

4.4.2 Strip Width /0mm Depth Ratio

ACCEPTABLE WIDTH / DEPTH RATIOS

digitally to obtain the Gaussian curvature at the polygon location. These samples were tested -20mm Experiment Description: This experiment against the target Gaussian curvature for a TARGET DEVIATION determined how the strip width-to-depth ratio 7-sided woven artifact found in Experiment -40mm affected the Gaussian curvature of a woven 4.4.1. 2.6 : 1 4.6 : 1 5 : 1 6.5 : 1 8.75 : 1 12.5 : 1 artifact. Experiment Results: The experiment showcased epth Ratio: 6.5:1 om Digital: 15mm Experiment Set-up: The data from this test WIDTHall/ DEPTH strip RATIO width-to-depth ratios above 6.5:1 created a consistent curvature with less than informed the minimum strip width-to-depth 4 ratios in the computational workflow. Six strip a 1.5x10 deviation from the control surface’s width-to-depth ratios were tested, ranging from Gaussian curvature. There were no meaningful 2.6:1 to 12.5:1. Strip widths of 4mm, 7mm, differences to the curvatures of artifacts with and 10mm and strip depths of 0.8mm and ratios above 6.5:1. As such, 6.5:1 was the 1.5mm were used to create the required range of minimum required strip width-to-depth ratio ratios. All samples maintained a central 7-sided to obtain an accurate morphology. The data polygon and 40cm strip length. Once woven, from this test was used to inform the minimum these artifacts were 3D scanned and recreated strip width to depth ratios in the computational workflow.

77 Bhagat | Pan | Wong

4mm Width / 0.8mm Thickness

4mm Width / 1.5mm Thickness

Deviation from Digital Model: 35mm

Deviation from Digital Model: 34mm

7mm Width / 0.8mm Thickness

7mm Width / 1.5mm Thickness

Deviation from Digital Model: 14mm

Deviation from Digital Model: 22mm

10mm Width / 0.8mm Thickness

10mm Width / 1.5mm Thickness

Deviation from Digital Model: 13mm

Deviation from Digital Model: 15mm

Width / Depth Ratio: 5:1

Width / Depth Ratio: 2.6:1

Width / Depth Ratio: 8.75:1

Width / Depth Ratio: 4.6:1

Width / Depth Ratio: 12.5:1

7mm Width

Width / Depth Ratio: 6.5:1

Target Curvature Actual Curvature

10mm Width

RGET TURE

Figure 47: Strip Width to Depth Ratio: Woven Samples -0.003 -0.002

The P2 Tower

4.4.3 Weave Density for 3D Printing: Material Sagging Experiment Description: This experiment determined how weaving density affected material sagging through the openings of a woven artifact. This test worked in conjunction with Experiment 4.4.4 to determine appropriate weaving densities for 3D printing. Experiment Set-up: Three samples were tested with 2cm (0.8mm thick), 3cm (1.5 mm thick), and 4cm (3mm thick) openings. Varied thicknesses were used based upon previous

4.4.4 Weave Density for 3D Printing: Minimal Deformation Experiment Description: This experiment determined how weaving density affected the artifact’s deformation from the weight of 3D printed material. This test worked in conjunction with Experiment 4.4.3. Experiment Set-up: Three samples were tested with 2cm (0.8mm thick), 3cm (1.5 mm thick), and 4cm (3mm thick) openings. Each artifact was 3D scanned afterwards to record the artifact deformation. Clay acted as a proxy material, as stated previously. Experiment Results: The larger openings deformed the least, since they were fabricated from thicker, more structurally stable strips. However, these artifacts performed poorly

4.4.5 Calibration of the Robot and Woven Artifact The team recognized the difficulty in calibrating an unknown object’s location in space when using a robotic arm to 3D print. An inaccurate calibration leads to large imperfections and print path deviations, which invalidates the results of the experiment. To mitigate this issue, the team utilized single objective optimization with Wallacei. First, the object was placed within the robot’s reach. The robot’s tool center point (TCP) was then located in multiple positions on the surface of the object, providing a data set for the object’s physical position. These points were then modeled digitally, and their distances

experiment results. Each artifact was 3D scanned afterwards to record the material sagging. Clay acted as a proxy material for concrete due to limited facility capabilities. As such, future experiments should translate the data from clay to concrete. Experiment Results: The smaller openings produced the least material sagging due to the smaller gaps. However, the artifact began deforming significantly under the clay’s weight, so Experiment 4.4.4 was required to comprehensively select weaving densities for 3D printing.

during Experiment 4.4.3. As such, a balance is required between material sagging and structural stability. To study both parameters comprehensively, the team analyzed the ratio between the weave opening size (related to material sagging) and strip depth (related to structural capacity), finding the 3cm/1.5mm artifact performed the best for both parameters. As such, a 20:1 ratio between the opening size and strip depth provided the best 3D printing ability while minimizing deformation. While these experiments produced viable results for material sagging and artifact deformation, the lack of test samples reduced the accuracy of the results. Additionally, the team recognized concrete behaves differently than clay, so a new set of experiments with proper materials is necessary to create a more useful data set.

from the original digital model were calculated. Finally, single objective optimization was performed to minimize this distance deviation, with translational and rotational movements as genes. In doing so, the team accurate placed and oriented the digital twin model. While this method worked well for the 3D printing experiments, some limitations reduced the accuracy of this process. First, the robot may not have access to all necessary points for digital twin adjustment. Second, the digital model may not be morphologically accurate, causing an inability to re-orient the digital model. In this case, it may be necessary to recreate a new digital twin from the targets.

3cm Weave Opening

4cm Weave Opening

2cm Weave Opening

3cm Weave Opening

4cm Weave Opening

2cm Openings / 0.8mm Thickness

4cm Openings / 2mm Thickness

3cm Openings / 1.5mm Thickness

Figure 49: Weaving Density for 3D Printing: Woven Samples

end

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0mm 48: Weaving Density: Material Sagging Experiment Results (4.4.3) Figure

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10mm 0mm 2cm Opening

3cm Opening

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WEAVE OPENING SIZE Figure 50: Weaving Density: Deformation Experiment Results (4.4.4)

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2cm Weave Opening

The P2 Tower

Parallel Joint System

Perpendicular Joint System

Figure 51: Parallel and Perpendicular Joint Systems

4.4.6 Joint System In conjunction with the weaving parameter experiments, the team developed a joint system which connected parallel and perpendicular surfaces. These joints were crucial for the fabrication of architectural scale elements since their sizes typically exceeded the limits of robotic arm reaches and transportation equipment. As such, all large-scale, woven design were discretized into smaller elements to join together on site. As such, the team created one parallel and perpendicular joint which takes advantage

of the bamboo’s weaving pattern to create a seamless single material joinery system. The weaving samples joined together by weaving all exposed ends alongside the existing strips in the mate surface. This process not only continued the weaving pattern, but also created a large amount of friction to secure the two elements in place. As such, no glue or reinforcements were necessary.

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PHYSICAL MODEL

DIGITAL MODEL

Kangaroo: Physics Simulator

INTERSECTIONS AS ANCHORS BAMBOO STRIP PROPERTIES Young’s Modulus: 11GPa 1mm thick | 10cm wide

Figure 52: Digital to Physical Translation

4.4.7 Digital to Physical Translation Once each parameter was studied in isolation, a computational workflow was developed which emulated the bamboo weaving’s behavior. This was done using a physics simulator, Kangaroo. The strips were modeled in 2D and given a

bamboo strip’s Young’s Modulus of 11GPa.2 An anchor was placed at each line intersection to emulate the woven nature of the system. The physics simulator ran for 5,000 iterations to obtain the final 3D result. The six physically woven samples from Experiment 04.04.1 were recreated digitally to test the workflow. A comparison of the physical and digital samples showed a small margin of error, validating the computational workflow.

Tutea Richmond et al., “Thermal and Mechanical Performances of Bamboo Strip,” Materials Research Express, February 2021, 0, https://doi.org/10.1088/2053-1591/abe060.

82 The P2 Tower

PHYSICAL SAMPLES

Figure 53: Physically Woven Samples

GAUSSIAN CURVATURE

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NUMBER OF SIDES PHYSICAL SAMPLES DIGITAL SAMPLES

Figure 54: Difference in Gaussian Curvature

DIGITAL SAMPLES

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Figure 55: Digitally Woven Samples

STRIP WIDTH / DEPTH RATIO

DEVIATION FROM TARGET GAUSSIAN CURVATURE

-0.003 -0.002

ACCEPTABLE WIDTH / DEPTH RATIOS

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WIDTH / DEPTH RATIO PHYSICAL SAMPLES DIGITAL SAMPLES

Figure 56: Difference in Strip-to-Depth Ratio

The P2 Tower

Bibliography Mulyana, B., and R. Reorita. “Mathematical Expression of Internode Characteristics of Yellow Ampel Bamboo (‘Bambusa Vulgaris’ Var. Striata).” Series II: Forestry Wood Industry Agricultural Food Engineering, June 28, 2022, 43–56. https://doi.org/10.31926/but. fwiafe.2022.15.64.1.4. Richmond, Tutea, Louise Lods, Jany Dandurand, Eric Dantras, Colette Lacabanne, Jean-Michel Durand, Edouard Sherwood, and Philippe Ponteins. “Thermal and Mechanical Performances of Bamboo Strip.” Materials Research Express, February 2021, 0. https://doi.org/10.1088/2053-1591/abe060.

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05 Design Development

5.1 Tower Morphology 5.2 Structural System 5.3 Public-Private Distribution 5.4 Progrmmatic Topology 5.5 Space Organization 5.6 Material Fabrication System

The P2 Tower

RESEARCH DEVELOPMENT

DESIGN DEVELOPMENT

DESIGN PROPOSAL

BAMBOO INTERNODE EXPERIMENT

TOWER EVOLUTIONARY ALGORITHM

TOWER MORPHOLOGY

CFD NEURAL NETWORK EXPERIMENT

STRUCTURE EVOLUTIONARY ALGORITHM

STRUCTURAL SYSTEM

CO-EVOLUTIONARY EXPERIMENTS

PUBLIC PRIVATE EVOLUTIONARY ALGORITHM

PRIVATE-PUBLIC DISTRIBUTION

TOPOLOGICAL RELATIONSHIPS EXPERIMENTS

VERTICAL TOPOLOGICAL RELATIONSHIPS EVOLUTIONARY ALGORITHM

PROGRAMMATIC TOPOLOGY

SPACE ORGANIZATION EVOLUTIONARY ALGORITHM

SPATIAL ORGANIZATION

VARIABLE CONTROL EXPERIMENTS

COMPONENT WEAVING PATTERN EXPERIMENT

STRUCTURAL ANALYSIS EXPERIMENT

MATERIAL FABRICATION SYSTEM

PHYSICAL MODEL EXPERIMENTS

Figure 57: Scope of Design Development Phase

Overview Once the exploratory experiments were completed, higher level studies were conducted to investigate and connect the tower’s systems more deeply. In this phase, each experiment developed the final workflow for formulating each of the six major sections of the tower

design. Each workflow was interconnected with the others to create a seamless, holistic system, where outputs of one feed directly into the next. Once developed, the comprehensive workflow was tested through a case study tower in the Design Proposal phase.

AL ORGANIZATION ATI SP

SOCIABILITY SCORE

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VATE-PUBLIC D I S T PRI RIB U

DECADES

MATIC TOPO RAM LOG OG Y PR

MONTHS

N TIO STRUCTURAL SYSTEM

FABRICATION SYSTEM

Figure 58: Tower Design Workflow

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TOWER MORPHOLOGY

The P2 Tower

5.1 Tower Morphology Experiment Description: This experiment developed a workflow to generate various tower design options which morphologically responded to the environmental conditions of Hong Kong. The experiment integrated the resultant equation from Experiment 4.1.1.

to-width ratio, branching arm conditions, segmentations, and total height. The information from these genes passed through the bamboo internodal equation to determine the locations of the major segments of the tower and the lateral bracing.

Experiment Set-up: The experiment utilized a multi-objective EA using Wallacei with the default algorithm parameters to generate tower morphologies optimized towards four fitness objectives: maximized daylighting during the winter, maximized surface area-to-volume ratio, minimized wind vector angle deflection, and maximized floor-to-area ratio. The EA ran for 50 generations with 25 individuals per generation, with a search space size of 6.5x1016. FC1 was calculated using Ladybug and weather data from a Hong Kong weather file for the period from September to March. FC2 was calculated by dividing the total surface area (m2) of the tower by its total volume (m3). FC3 was calculated by measuring the average difference between the normal vector at multiple points along the east-facing portions of the tower and a due east vector. FC4 was calculated by contouring the tower at a distance determined by a gene, summing the total gross floor area, and dividing this total by the area of the site. The tower design was grounded in the existing Harmony tower block. Starting with a base square, the genes control the area, length-

Experiment Results: The EA generated 162 pareto front members. FC2 and FC3 optimized over the 50 generations while FC1 and FC4 failed to optimize, highlighting a strong conflict between these criteria and the others. The pareto front members demonstrated a diversity of design options, verifying its ability to provide a range of solutions to address different sociability needs of the occupants. This morphology generation process generate site specific tower forms which respond to local environmental conditions and sociability needs, as demonstrated in the Design Proposal. The morphologies gained from this phase fed into a sequential simulation to generate the structural system.

91 INPUT INFORMATION

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URBAN CONTEXT

FC01 | Maximized Daylighting in Winter (hrs)

ENVIRONMENTAL CONDITIONS

g1 | Footprint Area (m2)

FC02 | Maximized SA:V Ratio (m3 / m2)

g2 | Length:Width Ratio

g3 | Auxillary Tower Selection

g4 | Segment Count

FC03 | Minimized Wind Vector Deflection (º)

g5 | Structural Height (m)

FC04 | Maximized Floor-to-Area Ratio (m2/m2)

g6 | Auxillary Tower Heights (m)

g7 | Maelstrom Location (x,y) g8 | Maelstrom Radius (m)

g9 | Edge Fillet Radius (m)

sequential simulation

STRUCTURAL SYSTEM

Figure 59: Tower Morphology Evolutionary Algorithm Set-up

The P2 Tower

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-6167174 -1254142737350735011752208 5970026 4001336 3009061

2411133

2011442 1725420

1510615

1343372 1209470

FC1 | Max Total Daylighting (kWh) Figure 60: Tower Morphology Evolutionary Algorithm Results

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0.164

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0.0414

0.0414 0.0348 0.0348 0.03

0.03 0.0264 0.0264 0.0236

0.0236 0.0213

0.0213 0.0194

0.0194 0.0178

0.0178 0.0165

0.0165 0.0153

0.0153 0.0143

0.0143 0.0134

FC3 FC | Min | Min Wind Wind Vector Vector Angle Angle (º) (º) 3

0.0134 0.0127

0.0127

-1.22

-1.22 -1.91

-1.91 -4.4

-4.4 14.31

14.31 2.72

2.72 1.5

1.5 1.04

1.04 0.794

0.794 0.642

FC4 FC | Max | Max FARFAR 4

0.642 0.539

0.539 0.465

0.465 0.408

0.408 0.364

0.364

The P2 Tower

5.2 Structural System Experiment Description: This experiment developed a workflow to generate a structural system for the exoskeleton which responded to the dynamic wind loads in Hong Kong. It utilized a sequential simulation on top of the previous tower morphology EA, whose gene ranges were optimized and shortened based on the ranges of its pareto front members, to find an optimal solution for both the tower morphology and structural system. This study integrated findings from the bamboo internode experiment and the CFD ANN experiment from the Research Development phase to respond to wind loads more accurately. Experiment Set-up: The experiment utilized a sequential, multi-objective EA using Wallacei with the default algorithm parameters to generate an exoskeleton structural system optimized for two fitness objectives: minimized deformation and minimized embodied carbon. The EA ran for 25 generations with 10 individuals per generation, and had a search space size of 4.2x1036. FC 1 was calculated using FEA using Karamba3D with an Eastern wind load of 0.87 kN/m2 which scaled up to 4.2 kN/m2 along the vertical height of the structure. The wind loads were obtained from the ANN developed previously. The structure had fixed supports in its corner vertices on the ground. FC2 was calculated by measuring the total volume of the exoskeleton and multiplying the mass (kg) by 1.42, the embodied carbon of steel (kgCO2/kg). To obtain the tower’s structure, FEA was performed on the base tower morphology, and the utilization of a 10cm shell was mapped to extract the points of high compression and

tension. These points were used to determine the principal stress lines (PSL) passing through them. Then, these PSL were voxelized using Dendro by a gene controlling the rationalization iterations and the voxel radius. From the mesh generated through this process, the medial skeleton was extracted as basis for the structural system, maintaining the topological connections of the original PSL to maintain a similar structural performance. Experiment Results: The EA generated 62 pareto front members. FC2 optimized quite well over the 50 generations, while FC1 marginally improved. These results highlight the strong conflict between the two fitness objectives. Looking at the morphologies of the pareto front members, it was observed that the fitness objectives were achieved by minimizing the overall size of the tower morphology, an approach directly conflicting the original fitness objective for the tower morphology. Additionally, there was a lack of variation among the pareto front. Therefore, further consideration should be given to counter such occurrences, either by introducing another fitness objective or forcing null constraints on the algorithm. This workflow was used to generate contextspecific structural systems for towers on various sites, as demonstrated in the Design Proposal. The morphologies gained from this experiment fed into the public-private distribution experiment.

INPUT INFORMATION TOWER MORPHOLOGY

Bhagat | Pan | Wong

FC01 | Minimized Deformation (cm)

sequential simulation

Wind Profile Load

g1 | Utilization Density (%)

PSL Voxelization

steel g2 | Mesh Skeleton Rationalization

g3 | Structural Diameter (cm) g4 | Structural Thickness (cm)

PUBLIC-PRIVATE DISTRIBUTION

Figure 61: Structural System Evolutionary Algorithm Set-up

FC02 | Minimized Embodied Carbon (kgCO2)

Principle Stress Lines

The P2 Tower

Gen50

Gen0

-35.36

-26.47

-17.58

-8.69

0.202

9.09

17.98

26.87

35.76

44.65

FC1 | Min Deformation (cm) Figure 62: Structural System Evolutionary Algorithm Results

53.54

62.43

71.32

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Gen50 Gen50

Gen0 Gen0

-6077751 -6077751 -4497644 -4497644 -2917537 -2917537 -1337430 -1337430 242676 242676 1822783 1822783 3402891 3402891 4982998 4982998 6563105 6563105 8143212 8143212 9723319 9723319 11303427 11303427 12883534 12883534

FCFC | Min | Min Embodied Embodied Carbon Carbon (kgCO (kgCO e)e) 2 2 2 2

The P2 Tower

5.3 Private-Public Distribution Experiment Description: This experiment developed a workflow to distribute the tower’s private and public zones throughout the tower, such that each responds appropriately to the sociability needs of the residents. The mutualism co-evolutionary method was selected for this experiment based upon the previous studies. Experiment Set-up: The experiment started with the morphology and structure generated from Experiment 5.1,5.2. The spaces between the structural segments were voxelized into 5mx5mx3.5m sized voxels, which corresponded to the scale of the program spaces. Then, random starting voxels were selected within each tower segment, from which the voxels randomly aggregated to take over the three-dimensional space. Each tower segment had competing aggregations growing simultaneously, representing the private and public distributions. A sequential, mutualism CoEA was employed to optimize the distributions throughout the tower towards the goals of maximized public distribution, maximized public segment

connections, maximized housing density, and maximized private program proximity. Genes controlling the starting seed locations and growth parameters dictated the aggregation of the voxels, enabling them to compete with one another over the finite space. Experiment Results: Similarly to the initial CoEA experiments, all fitness criteria mildly optimized. This showcased the “ideal team” mindset which allowed for two systems to improve in conjunction. This workflow distributed public and private spaces in the tower, which was demonstrated in the Design Proposal. The morphologies gained from this experiment fed into the program topology and spatial organization experiments.

INPUT INFORMATION TOWER MORPHOLOGY

Bhagat | Pan | Wong

FC01 | Maximized Public Distribution

STRUCTURAL SYSTEM

FC02 | Maximized Public Segment Connections

Base Tower Morphology

FC03 | Maximized Housing Density

Tower Segmentation

g1 | Public Start Point

FC04 | Maximized Private Program Proximity

g2 | Private Start Point

g3 | Public Start Count g4 | Private Start Count g5 | Public Growth Rate g6 | Private Growth Rate PROGRAM TOPOLOGY

SPATIAL ORGANIZATION

Figure 63: Public-Private Distribution Evolutionary Algorithm Set-up

The P2 Tower

100

Gen50

Gen0

-672.68

501.91

182.77

111.73

80.45

62.86

51.58

43.73

37.96

33.53

30.03

27.19

24.84

-0.775

FC1 | Max Percentage Public

Figure 64: Public-Private Distribution Evolutionary Algorithm Results

-1.19

-2.57

16.33

1.95

1.04

0.707

0.536

0.432

0.362

FC2 | Max Housing Density

0.311

0.273

0.243

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Gen50

Gen0

-18.24

-66.76

40.2

15.45

9.56

6.92

5.43

4.46

3.79

3.29

FC3 | Max Private Proximity

2.91

2.61

2.36

-6.01

-7.86

-11.34

-20.38

-100.25

34.34

14.66

9.32

6.83

5.39

FC4 | Max Public Segment Count

4.45

3.79

3.3

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5.4 Programmatic Typology Experiment Description: This experiment developed a workflow to create programmatic relationships within the tower to respond to the residents’ sociability needs. The experiment utilized the SWN workflow developed previously but introduced an additional vertical network system to connect program segments together. Experiment Set-up: This experiment created a logic of connectivity between architectural functions to achieve a well-connected, yet efficient, network. The network was controlled through the following genes: the radius of connectivity with other points, the number of connections to other points, and the rate of reduction for connections. Connection rules were integrated within the SWN to facilitate network creation. These genes were manipulated to achieve a maximized clustering of points, a minimized path count, a maximized path weighting, and a node weighting closest to the required program sociability score.

Experiment Results: This experiment showcased the SWN’s ability to create highly optimized topological relationships when using an evolutionary algorithm. All fitness criteria mildly optimized and the pareto front members show a variety of connection conditions, facilitating a range of solutions to address different sociability needs of the occupants. This program network generation process applied to any base program distribution, as demonstrated in the Design Proposal. The networks gained from this phase fed into the spatial organization system to translate the relationships into usable space.

INPUT INFORMATION

103

TOWER MORPHOLOGY

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PUBLIC-PRIVATE SEGMENTS

C G B H A I O J N E

C(i) = E(i) / T(i)

g1 | Distance Between Points

FC01 | Maximized Cluster in Network

A J

C G

B H A I E

N K L

B H A

g2 | Proportional Line Reduction

I O J

FC02 | Minimized Path Count

O J

G B

2 E

5 4

N L

J N

g3 | Random Connection with

Other Points

2.22 3.87

SEGMENT A

4.03

vertical connection

2.9

5.5

2 5

4.03

3.88

4 2

4.55 5

SEGMENT B

1.76

1 2 2.33

4 1 2.01

g4 | Vertical Connection with Other Segments

SPATIAL ORGANIZATION

Figure 65: Programmatic Topology Evolutionary Algorithm Set-up

FC03 | Maximized Path Weight

A I

3 2.05

5.02

3.1

2.85

FC04 | Minimized Difference Between Sociability Scores

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Gen50

Gen0

0.0544 8.54e-0034.63e-003 3.18e-003 2.42e-003 1.95e-003 1.64e-003 1.41e-003 1.24e-003 1.10e-003 9.94e-0049.05e-0048.31e-004

0.631

FC1 | Max Cluster Value

Figure 66: Programmatic Topology Evolutionary Algorithm Results

0.589

0.553

0.52

0.492

0.466

0.443

0.422

0.403

FC2 | Min Path Count

0.385

0.369

0.355

0.341

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Gen50

Gen0

15.08

13.67

12.5

11.51

10.67

9.95

9.31

8.75

8.26

FC3 | Max Path Weight

7.82

7.42

7.06

6.74

0.0203

0.0166

0.0141

0.0122

0.0108 9.68e-0038.76e-0038.00e-0037.37e-0036.82e-0036.35e-0035.95e-0035.59e-003

FC4 | Min Sociability Score Difference

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5.5 Spatial Organization Experiment Description: Based upon the topological program relationship, they were translated into physical space. This experiment created a workflow to generate a tower program layout that met the defined topological relationships, program areas, and program counts. Experiment Set-up: A multi-objective optimization was conducted using Wallacei with default algorithm settings to optimize for the following fitness criteria: minimized topological relationships difference, minimized program area difference, and minimized program count difference. To obtain the program layout, the public and private segments defined in Experiment 5.3 were voxelized and start points for each program are placed. Each voxel was 5mx5mx3.5m, which followed the dimensions of one program space, and all start point placements were random. All programs were grown incrementally within the defined segment. The genes controlled the program start location, number of iterations for growth, and growth parameters. These

voxelized spaces were used as the locations for each program component, creating usable spaces within the tower design. Experiment Results: The results of the EA showed the pareto front members achieved the desired relationships and spatial organization criteria as each fitness criteria optimized well. As such, this process proved to be an acceptable method for generating program layouts within the tower. However, it should be noted some generated individuals may not meet every topological relationship connection. As such, further research is needed to mitigate this issue. This process applied to any topological network to generate programs which meet the occupants’ sociability needs, as was demonstrated in the Design Proposal.

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INPUT INFORMATION PUBLIC-PRIVATE DISTRIBUTION

FC01 | Minimized Topological Relationships Difference

PROGRAMMATIC TOPOLOGY

g1 | Program Count

FC02 | Minimized Program Area Difference

g2 | Program Start Point

g3 | Program Placement Iterations g4-12 | Voxel Selection Index g 13-21 | Voxel Selection Direction

FC03 | Minimized Program Count Difference

g22 | Program Maximum Area

Component Placement

COMPONENT DESIGN

FABRICATION SYSTEM

Figure 67: Spatial Organization Evolutionary Algorithm Set-up

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Gen50

Gen0

-32.36

-16.51

-0.662

13.19

31.04

46.89

62.74

78.59

94.44

110.291

141.99

157.84

FC1 | Min Program Relationship Difference

Figure 68: Spatial Organization Evolutionary Algorithm Results

86.41

218.82

351.22

483.63

748.44

880.84

1013.25

1145.65

1278.06

1410.46

FC2 | Min Program Area Difference

1542.87

1675.22

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Gen50 Gen50

Gen0Gen0

0.109

0.109 0.006

0.006 0.003

0.003 0.07

0.127 0.07

0.127 0.174

0.174 0.221

0.221 0.268

0.268 0.315

0.315 0.3621 0.3621 0.409

0.409 0.456

FC3 FC3 | Min| Min Room Room Distribution Distribution Difference Difference

0.456

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MODULE

COMPONENT SPATIAL ORGANIZATION

Figure 69: Component Morphology and Placement

Component Design A component was designed to formalize the voxelized program areas within the tower from Experiment 5.5. One component occupied the space of one voxel and attached to the tower’s substructure. The goal of the design was to achieve a modular, space-filling, component which can be woven and has usable horizontal floor area. The rhombic dodecahedron was selected as the geometry for the component due to its space-

filling nature, large usable floor area, and feasible print and weave angles. Additionally, this geometry aggregated to create continuous horizontal floor surfaces which increased its functionality when used for programmed space. The component dimensions are 5m x 5m x 3.5m, which were determined by considering both the minimum area required for usable program and the minimum dimensions required to physically weave the component. However, a component of this size is out of range for a robotic arm to feasibly 3D concrete print on, so the geometry was sub-divided for ease of fabrication.

5.6 Material Fabrication System

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Component Material System The component was made of bamboo weaving and 3D printed concrete. The bamboo acted as formwork and rebar to minimize material usage, while maintaining structural stability. A second layer of bamboo was integrated within the structural studs on the inside, as a

base to weave in interior panels. This created a seamless, single material joinery system. Multiple modules joined together by weaving the exposed bamboo strips together and sealing the seam with a layer of concrete.

MODULE

3D PRINTED CONCRETE

SECTION DETAIL

6cm

WOVEN BAMBOO FORMWORK 4cm 3.5m

SECT

COMPONENT

3D PRINTED CONCRETE shell

6cm

WOVEN BAMBOO formwork

MWORK

3D PRINTED CONCRETE

4cm

studs

WOVEN BAMBOO joinery

SECTION THROUGH SHELL Figure 70: Material Fabrication System

DIGITAL TO PHYSICAL

3D PRINTING WEAVE DENSITY

JOINT SYSTEM

STRIP WIDTH / DEPTH

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GAUSSIAN CURVATURE

112

Figure 71: Weaving Pattern Influence from Experiments

DEVIATION OF WOVEN MODEL

DEVIATION OF PHYSICAL MODEL (mm)

100mm 80mm 60mm 40mm 20mm 0mm Left Edge

Center

Right Edge

LOCATION OF TEST POINT

Figure 72: Component Weaving Experiment Results

accuracy of the computational workflow. 5.6.1 Component Weaving Pattern the The discrepancy between the two models was Experiment Description: This experiment created the component’s weaving pattern using the established computational workflow and knowledge gained from the initial variable control experiments in the Research Development phase. Experiment Set-up: The weaving pattern was tested through the creation of a physical prototype. The prototype was 3D scanned and compared to the digital model to determine

recorded, showcasing areas of deviation.

Experiment Results: Some larger areas of deviation were found, particularly towards the outer edges of the component. This was mainly due to the digital workflow not having the capability to account for the inherent error in the weaving process caused by uneven material widths and variable Young’s moduli for each bamboo strip. While the workflow produced decently similar result, additional experiments are required to increase its accuracy.

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Bhagat | Pan | Wong

12cm Concrete Shell

114

8cm Shell + 4cm Studs

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Max. Deformation = 0.109 cm

0.112cm

Wind Load 0.5kN/m2

Gravity Load

3.5m

0cm

-0.112cm

10cm Concrete Shell + Bamboo Weaving 6cm Shell + 4cm Studs

Max. Deformation = 0.112 cm

0.112cm

Wind Load 0.5kN/m2

Gravity Load

3.5m

0cm

-0.112cm

Figure 73: Component Structural Analysis

5.6.2 Component Structural Analysis Experiment Description: To analyze the feasibility of the component, its structural performance was tested against a simple concrete shell. This experiment aimed to understand if the proposed fabrication system worked similarly to a standard concrete system. Experiment Set-up: A finite element analysis was performed on two component modules using Karamba3D: one with a 8cm concrete shell and 4cm studs and another with a 6cm concrete shell with a layer of bamboo formwork and 4cm studs. A gravity load and wind load (0.5kN/m2)

was applied to each model with simply supported anchors at each bottom corner. The maximum deformation for each model was recorded and compared. Experiment Results: The experiment showcased that the thinner concrete shell and bamboo system had a similar maximum deformation to the standard concrete shell. As such, it was feasible to use the bamboo and concrete system for the component design. This material system improved upon a traditional concrete shell due to its lightweight nature, reduced embodied carbon, easy fabrication process, and ability to use weaving as a singlematerial joinery system.

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Figure 74: Component Slab Test Model

5.6.3 Component Slab Section Test Experiment Description: This experiment tested the feasibility to create the proposed multilayer concrete and bamboo system through the fabrication of a simple section. Experiment Set-up: One slab portion was fabricated with a concrete slab with embedded bamboo formwork, concrete studs, and one inner layer of bamboo for partition attachment.

This model tested concrete’s ability to bond with bamboo and the critical stud to bamboo condition. Casted concrete was used instead of 3D printed concrete due to limited facility capabilities. Experiment Results: The experiment showcased a strong connection between the concrete and bamboo. The concrete flowed between the woven cells, which locked the bamboo in place. As such, this experiment proved the viability of the proposed system, allowing the team to move forward to a large-scale mock-up.

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5.6.4 Large Scale Mock-Up Using the data and results from all the fabrication experiments, the team created a 1:5 scale mock-up of the component’s most critical conditions. The model showcased the viability of the designed component and material fabrication system.

06 Design Proposal

6.1 Site Selection 6.2 Case Study 6.3 Life in the P2 Tower 6.4 Adaptable System

Chuk Yuen United Village

Ngau Chi Wan Village

Cha Kwo Ling Village

Chuk Yuen United Village

Ngau Chi Wan Village

Site Selection The Hong Kong government slated three existing urban villages for demolition, with plans to replace them with new public tower blocks by 2029. As such, these sites provided an opportunity to introduce the P2 Tower in Hong Kong. The team specifically selected the Chuk Yuen United Village site for the case study due to its central location and its connectedness with other housing blocks and public spaces.

Cha Kwo Ling Village

Chuk Yuen United Village

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1957

the British Hong Kong Government ordered the compulsory acquisition and clearance of the Chuk Yuen Wooden Houses Area, including the village houses of the indigenous residents of Chuk Yuen Heung, for the establishment of the resettlement area.

1958-1961

The cleared lots in the southern part of Chuk Yuen Village were successively built into “Wong Tai Sin Lower Estate” and “Wong Tai Sin Upper Estate”.

1980

The Government started to demolish the northern part of the Chuk Yuen Resettlement Area and rebuilt Chuk Yuen North Estate and Chuk Yuen South Estate, with a number of bus routes travelling to and from different parts of Hong Kong.

2019

The Chief Executive, Mrs Carrie Lam, announced in the Policy Address that she plans to resume private land in three major urban squatter areas - Cha Kwo Ling Village, Ngau Chi Wan Village and Chuk Yuen Heung for the construction of public rental housing, HOS flats, GHOS flats and Hong Kong first-time home buyer flats.

Among them, located next to the Wong Tai Sin Temple, site area of 1 hectare, residential can be built floor space of about 807,300 square feet, the proposed construction of three blocks of 32-storey to 45-storey public housing, providing about 1,500 units, which can accommodate a population of about 4,050.

The P2 Tower

TOWER MORPHOLOGY

Application of Tower Workflow

124

2. STRUCTURAL SYSTEM

DECADES

N TIO

YEARS

SOCIABILITY SCORE

MATIC TOPO RAM LOG OG Y PR

MONTHS

AL ORGANIZATION ATI SP

VATE-PUBLIC DIST PRI RIB U

4. FABRICATION SYSTEM

Case Study The developed workflow presented in the Design Research phase was implemented on the Chuk Yuen United Village site as a case study. This showcased the application and functionality of the workflow in a site-specific context. The

case study viewed the tower’s sociability needs through the lens of four family types: young couple, couple with children, empty nesters, and elderly couple. Each portion of the tower design was implemented based off one moment in time for these residents. Then, further adaptations occurred over the span of months, years, and decades as their sociability needs changed.

Step 02: The structure design was heavily influenced by the high Eastern wind loads on site. This created variations in density across the structural system to sufficiently counteract the uneven load distributions.

Step 03: The program distribution, program topology, and space organization was largely influenced by the sociability needs of the tower’s residents. Certain programs were located in higher densities in correspondence these requirements. For example, families with children lived near a higher density of schools and libraries than other residents. However, it was mandatory to ensure that all residents had access to every program type in some capacity.

Step 04: Finally, the component was introduced in the locations of each program voxel to create usable spaces for the residents. Internal partitions were also created at this stage to develop interior spaces into functional rooms.

Figure 75: Workflow Applied to Case Study

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Step 01: The tower morphology was created based on influences from local site context and Hong Kong’s sunny, humid climate. This formed shorter branches on the South side to limit exposed tower surface area, yet shaded some portions of the facade.

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126

YOUNG COUPLE (30s)

COUPLE WITH CHILDREN (40-50s)

EMPTY NESTERS (60s)

ELDERLY COUPLE (70-80s)

use them the most and smaller pockets of programs are placed near those with less of a need. As such, the tower was tuned to the particular requirements of the residents at this moment in their lives.

Sports

Medical

Mechanical

Education

Working

Gathering

Nature

Food

Services

Leisure

Figure 76: Life in the P2 Tower

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Life in the P2 Tower

The impact of the proposed tower design workflow was seen in respect to the lives of the residents. Their local programs and conditions were particularly tailored to their specific needs, where large clusters of each program placed near the occupants who

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Spring is the right time for morning tea, and people set up their spaces well in advance for the arrival of spring. In the spring breeze, it seems as if the impatient Hong Kong has become gentle. The use of traditional teapots, teacups and bamboo steamers combined with a modern moveable space creates a new form of dining.

Summer, when parents move in for the summer holidays, the cool ventilation system and wellserviced facilities in a modern public building can make the season more relaxing for the elderly.

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Autumn, when children come home from school, the space needs to be changed for them, so that their creativity can be better stimulated. In the public space, there are also more people of the same age to play.

Winter is the time for hot pot. Hot pot brings cold people to gather together. A one sip brings back a feeling one immediately remembers. The transformed space can be made functional in just a few weeks, making it more suitable for the fastpaced city life.

Adaptable System

Once the tower was designed for the resident’s initial lifestyles, further adaptations were facilitated by the presence of certain trigger events. For example, changes in social behavior elicited adaptations to the tower’s public-private distribution or changes in family size sparked program adaptations, to name a few. As such, the initial tower design continued to grow with its residents.

Change in social priorities Change in demographics Change in behavior

Architectural Response

PUBLIC-PRIVATE DISTRIBUTION

DECADES

Trigger Event

Change in work/life balance Change in family age

PROGRAM TOPOLOGY

YEARS

Change in family size

Change in family daily habits Change in seasonal need Special activities

Figure 77: Adaptability of the P2 Tower

SPATIAL ORGANIZATION

Large scale events

MONTHS

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INTERWOVEN BAMBOO ATTACHMENT TO STRUCTURE INTERIOR PANEL

Figure 78: Component Design

Component Design The component design largely facilitated the tower’s adaptation. Its unique form is modular and space-filling, allowing for easy fabrication and re-configuration when new program is required. Additionally, the chamfered corner

facilitated new spatial connections which may otherwise be lost in traditional tower settings. The material fabrication system also increased the component’s adaptable functionality, where the inner woven bamboo layer easily allowed for changes in the interior layout due to its seamless single material joinery system.

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CONCRETE FACADE BAMBOO JOINERY

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CONCRETE STRUCTURE FLOOR

Figure 79: Exploded View of Component System

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Figure 80: View of Working Space

Adaptation: Months Timescale Over the timescale of months, a space’s program layout changed in response to the changes of residents’ local behaviors and needs. These architectural changes were facilitated by

changes in the interior partitions, which can be quickly switched out by residents. In this example, one space began the year as a bustling office space, full of both collaborative work spaces and more private pods. Residents can pick and choose how they work, as the space provided a diverse range of working lifestyles.

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Figure 81: View of Restaurant

Adaptation: Months Timescale During the summertime, the residents work less and long for more social spaces. In response, the workplace’s interior changes to become a

lively restaurant with large, open spaces for gathering, eating, and socializing. Tables line the interior, facilitating dynamic conversations all evening.

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Figure 82: View of Library

Adaptation: Months Timescale As the Fall approaches, the local residents began to require an educational space for their children to study. Over the next few days, the

once restaurant transformed into a library, with small, private pockets of bookshelves and desk spaces. Now, children were free to study, read, and learn throughout the school year.

Adaptation: 1 Year

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142

I finally own a small house in Hong Kong, which is not very big, but it is sufficient for my daily needs. For a high rise public housing unit, the public space is very convenient, and it can evolve as I do.

Single Area: 20m2

Living Room Bathroom Master Bedroom

As a single person flat, it contained functions that only need to satisfy the basic needs of the individual, and to relieve the pressure of people who have a pressing need for housing and the emergence of a social movement. At the most basic level, people can move into a flat immediately at a relatively cheap price.

Adaptation: 3 Years

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Over time, I also found a roommate to share the room with, and together we enlarged the room to better fit two people. The communal space around us also allowed us to meet more people in our daily lives.

Shared Area: 40m2

Living Room Dining Room Bathroom Master Bedroom

The process of building from a studio flat to a shared flat allowed people to change according to their needs. As the size grew, the box can accommodate more personal space features to suit the needs of two people.

Adaptation: 5 Years

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After having a child, the focus of life changed completely. I have to keep an eye on my children’s schooling and life, and the facilities in the building allow me to form closer relationships with my children without the hassle of having to move to a neighbouring primary school.

Family Area: 60m2

Living Room Study Room Dining Room Bathroom Children’s Room Master Bedroom

With the emergence of children, the center of gravity of space changed, and families needed more gathering centers, the ‘public space’ of the home. As a family home, the rapid growth of children dramatically changed in space, and removable functional modules can be very good to meet the space changes.

Adaptation: 10 Years

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Finally, I have brought my parents to live with me, and the tower is very convenient for my elderly parents. With the excellent medical and service facilities, we can rest assured of our parents’ health. It was very convenient to expand the family and it made it possible for me to have my second child.

Extended Area: 120m2

Living Room Study Room Dining Room Bathroom Elderly Room Children’s Room Master Bedroom Storage Room Laundry Room

As a large family grew, the relationships between spaces became more complex and the number of functions required increased. But all spaces grew from the basic unit space, which in turn relieved the homeowner of much of the stress of standing in a high-density city.

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07 Discussion

7.1 Overview 7.2 Workflow 7.3 Computational Tools 7.4 Fabrication System 7.5 Case Study 7.6 Conclusion

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Overview In reimaging the relationship between private and public spaces, the P2 Tower stepped beyond traditional understandings of these spaces by locating them along a spectrum. Such a delineation provided a strong framework for developing a system which adapts along with changes in people’s sociability. Thus, the tower and its residents evolve together over time, and evolution becomes not only a computational tool but now a driving design methodology. Such a notion conceptually implies an architecture which is no longer static, where design characteristics gain transiency. It originates from the bottom up, as the users initiate, implement, and drive the changing architecture, much in the original spirit of Archigram and Metabolists. Therefore, the research calls for the idea of an evolving architecture to enable the occupants to determine the futures of the spaces they inhabit.

Workflow By approaching the design of the P2 Tower from the perspective of a flexible workflow, the research conducted was not merely relegated to a site-specific solution. Instead, it afforded the opportunity for this research and these tools to address modern challenges of densification in other dense cities around the world. While Hong Kong proved to be a well-suited case study, the workflow’s flexibility lied in the tools employed, which provided wide ranges of solutions and opportunities. Further experiments should attempt to employ it for different sites and unique design considerations. Such validation was not a part of the research but would provide a strong basis for understanding the bounds of the system, particularly focusing on when and

where it begins to fail. These inflection points would provide a strong insight into the elements of the workflow which are not as flexible as conceptually intended. While the workflow derived its flexibility from the computational tools and fabrication system, these elements simultaneously behaved as its restraints because the workflow lacked a strong degree of clarification between the fixed and adaptable elements. Such a level of abstraction prevented the workflow from truly becoming as flexible as desired. As such, it limited the ability for other architects and urban planners to easily utilize the workflow as a new design tool. While it appears obvious certain sitespecific design decisions, such as the use of bamboo weaving, would be changed in other contexts, what is not obvious are the alternative options or if such options exist at all. Further research should clarify which elements of the workflow adapt to new contexts and how one might select alternative options. Post-analyzing these alternative elements would then provide a strong insight and validation into the true flexibility of the workflow as a whole.

Computational Tools The co-evolutionary algorithm, the artificial neural network, and the small-world network, to name a few, enabled the workflow to respond to varying situations and changing design parameters. Such a deployment of computational tools highlighted both the applicability and the benefits of integrating these methodologies into the traditional design process of architects and urban planners. In the same way these tools empowered the research’s workflow to adapt to different scenarios, they offer architects and urban planners the opportunity to respond to

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On the other hand, a heavy reliance on these tools as design solution generators is severely misplaced and limits the design possibilities, which was demonstrated at numerous points throughout the research. The use of these tools requires architects and urban planners to shift their mindset from designing the solution to designing the problem environment. Failing to do so would hinder the potential of these tools and essentially pigeonhole the design. For example, the design of the tower’s structural system involved an extraction and rationalization of principle stress lines. The research utilized an evolutionary algorithm to optimize the structural system and this process, but such a specific design approach limited the solution set, which was reflected in lack of diversity amongst the Pareto Front members. Further research should examine and question the necessity of using computational tools at each stage of the workflow, balancing their affordances with their limitations. In doing so, the research begins to reimagine the role of the designer in a computation-driven design process. Additionally, the implication of randomness within these design tools requires further evaluation. From the use of the random walker algorithm to the small-world network, the workflow was littered with instances of randomness, but there was a lack of clarity upon its impact on the solution sets. The workflow utilized an evolutionary algorithm to seemingly

optimize such results into a relatively predefined solution range, but this implementation was a poor use of these tools. The solution sets lacked diversity and originality, providing merely a means to an end as opposed to the beginning of a design discussion. Instead forcing the randomness to generate a particular solution set, the research should have selectively employed randomness throughout the system to take advantage of its benefits and enable an adaptable architectural system. Further research should examine the area where randomness provides the most impact upon the workflow.

Fabrication System The methodology for testing and exploring the fabrication system was a solid process for understanding its limits and benefits. By deconstructing the parameters of the fabrication system and separating each into individual experiments, the research could develop a holistic knowledge base about the fabrication system, particularly in the relationship between parameters. This enabled the research to translate these parameters more easily into a computational workflow. However, while the methodology was methodical and comprehensive, it lacked a degree of specificity and scalability due to the limitations of the available tools and facility capabilities. From robotic 3D printing with clay instead of concrete to weaving plywood strips instead of bamboo strips, the use of proxy materials throughout the experiments, while relatively performative, lacked the scalability sought by the research. This discrepancy was particularly evident during the clay 3D printing experiments, where clay’s material behavior differed significantly from concrete, limiting its

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more commonplace design challenges such as climate adaptation or embodied carbon. Thus, the research exists not only as a potential solution to densification and urban living but also as a catalyst and proof-of-concept for integrating computational tools into the design process.

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applicability to simply tool path and 3D scanning studies. Further research should re-evaluate the fabrication system and its parameters with the intended material systems to revise the findings from this research.

Case Study The case study demonstrated a complete execution of the developed workflow for a sitespecific case and showcased a resultant design solution, providing a more tangible insight into the workflow. Architecturally, the interwoven nature of public and private spaces throughout the tower becomes quite evident when looking at the P2 Tower in section as well as the areas for growth and adaptation. In this sense, the workflow achieved the desired design goals. Yet, upon further reflection, the workflow optimized the tower for a single point in time, highlighting a paradoxical relationship between the computational tools as optimization tools and an adaptable architectural system. This discontinuity was mitigated, in part, by the fabrication system and the organization of the workflow itself, but the research begins to raise the question as to the applicability of these tools in developing more fluid design solutions. If it may be argued that such optimization by the tools enables an initial iteration of an adaptable architecture, then further research should investigate how the workflow or the computational tools are implemented, if at all, to determine the adaptations of the tower. Thus, the research and case study ask, “How does one balance optimizing a system while still providing the flexibility for it to adapt and still perform well?”

Conclusion The P2 Tower investigated the gap between the social affordance of the Hong Kong tower block and the people’s sociability needs. The proposed framework aimed to create a new design for public housing towers which meets the density needs of Hong Kong while also facilitating continuous spatial changes to match the needs of people over time. Looking ahead at future research, the team will explore the urban scale implications of this tower design framework during the M.Arch phase, understanding how a network of these public and private spaces affect the changing sociability and density needs of the city. Potentially, the M.Arch. scope may include a redesign of the city’s buildings, urban spaces, transportation systems, and infrastructure, to address the issue of densification and sociability more holistically. Other research can also explore this framework’s application to other dense cities. While some facets of the P2 Tower system are transferable, many aspects must adapt to local climate and context. As such, further explorations can facilitate framework adaptations which address the densification and sociability around the globe. In combination with this thesis, these future explorations help facilitate a built environment that continuously transforms with its occupants.

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Re-Neighboring the Vertical City